Page 1
Propositional Calculus II:Two more Rules of Inference/Inference Schemata
(conditional elim = modus ponens, proof by cases), Application to Additional Motivating Problems
Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science
Lally School of Management & TechnologyRensselaer Polytechnic Institute (RPI)
Troy, New York 12180 USA
Intro to Logic2/3/2020
Selmer Bringsjord
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No, it’s not logical to throw a bomb from the Kansas City 49-yard line @ 3rd and 10, with 1:49 to go.
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Re-re-re…orientation w.r.t. web pages …
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The Starting Code to Purchase in Bookstore
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The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
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The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The email address you enter is case-sensitive!
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The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The email address you enter is case-sensitive!Your OS and browser must be fully up-to-date; Chrome is the best choice, browser-wise (though I use Safari).
Page 8
The Starting Code to Purchase in Bookstore
Once seal broken on envelope, no return. Remember from first class, any reservations, opt for “Stanford” paradigm, with its software instead of LAMATM paradigm!
The email address you enter is case-sensitive!Your OS and browser must be fully up-to-date; Chrome is the best choice, browser-wise (though I use Safari).Watch that the link doesn’t end up being classified as spam.
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The Starting Code Purchased in Bookstore Should By Now’ve Been Used to Register & Subsequently Sign In
First batch of prop. calc. (Homework) Problems in;easiest starting place: switching_conjuncts_fine.
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E-Housekeeping Pts, Redux
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E-Housekeeping Pts, Redux
• Must input your RIN.
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E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
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E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
• Make sure browser fully up-to-date.
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E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
• Make sure browser fully up-to-date.
• Chrome best (but I use Safari).
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E-Housekeeping Pts, Redux
• Must input your RIN.
• Make sure OS fully up-to-date.
• Make sure browser fully up-to-date.
• Chrome best (but I use Safari).
• Always work in the same browser window with multiple tabs; must do this with email and HyperGraderTM & HyperSlateTM.
Page 16
Propositional Calculus II:More Rules of Inference
(conditional elim = modus ponens, proof by cases), Application to Additional Motivating Problems
Rensselaer AI & Reasoning (RAIR) LabDepartment of Cognitive ScienceDepartment of Computer Science
Lally School of Management & TechnologyRensselaer Polytechnic Institute (RPI)
Troy, New York 12180 USA
Intro to Logic2/3/2020
Selmer Bringsjord
Page 17
Last time we introduced and and lauded the power of oracles, and questions … and now … picking up where we left off …
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“NYS 3” RevisitedGiven the statements¬¬cc → a¬a ∨ bb → d¬(d ∨ e)
which one of the following statements must also be true?
¬ceh¬aall of the above
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“NYS 3” RevisitedGiven the statements¬¬cc → a¬a ∨ bb → d¬(d ∨ e)
which one of the following statements must also be true?
¬ceh¬aall of the above
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“NYS 3” RevisitedGiven the statements¬¬cc → a¬a ∨ bb → d¬(d ∨ e)
which one of the following statements must also be true?
¬ceh¬aall of the above
After last class, should have done …Exercise: Show in HyperSlateTM that each of the first four options can be proved using the PC entailment oracle.
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(and (not C) E H (not A))
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(and (not C) E H (not A))
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(and (not C) E H (not A))
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(and (not C) E H (not A))
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(and (not C) E H (not A))
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(and (not C) E H (not A))
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(and (not C) E H (not A))
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Proof Plan …
Sub-Proof
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Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
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Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
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Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
conditional elima.k.a., modus ponens
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Proof Plan …
Sub-ProofInstead of using the PC oracle, we can use a new inference rule:
conditional elima.k.a., modus ponens
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The Universe of Logics
Infinitary Finitary
Intensional ExtensionalDeductive InductiveDeductive Inductive
Symbolic Diagram Symbolic Diagram Symbolic Diagram Symbolic Diagram
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L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
Page 39
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
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The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Page 41
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Page 42
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
Page 43
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Page 44
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
Page 45
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">AAACPnicbVC7SgNBFJ31bXxFLW0Gg2AVdkXQRhRtLCwimAdkQ5i9mdXB2Z1l5q4kLPs5/oe9rRb+gNiIraWzMYVJPDBwOOeeudwTJFIYdN03Z2Z2bn5hcWm5tLK6tr5R3txqGJVq4HVQUulWwAyXIuZ1FCh5K9GcRYHkzeD+ovCbD1wboeIbHCS8E7HbWIQCGFqpWz71I4Z3BnR2lXczH3kfDWQ1rZILJiHP6Qn1o0D1s8RKyogixSQFa6YyNXm3XHGr7hB0mngjUiEj1LrlD7+nII14jCCZMW3PTbCTMY0CJM9Lfmp4wuCe3fK2pTGLuOlkw0NzumeVHg2Vti9GOlT/JjIWGTOIAjs5PGvSK8T/vHaK4XEnE3GSIo/hd1GYSoqKFq3RntAcUA4sYaBtC0DhjmkGaLsd21L8rU1o8pKtxpssYpo0DqqeW/WuDytn56OSlsgO2SX7xCNH5IxckhqpEyCP5Jm8kFfnyXl3Pp2v39EZZ5TZJmNwvn8AOVuyBg==</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
Page 46
The Universe of Logics
Infi Fi
Inte Exte
L!1!<latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit><latexit sha1_base64="6QTBLq7Snn0MqwYuB9YLScIUffM=">AAACHHicbVBNS8MwGE7n15xfVY8iBIfgabQi6HHoxYOHCe4D1lHSLN3CkqYkqTBKT/4P7171L3gTr4L/wJ9h2vXgNh8IPDzP+5UniBlV2nG+rcrK6tr6RnWztrW9s7tn7x90lEgkJm0smJC9ACnCaETammpGerEkiAeMdIPJTe53H4lUVEQPehqTAUejiIYUI20k3z72ONJjhWV6l/mpJzgZId+FM5L5dt1pOAXgMnFLUgclWr794w0FTjiJNGZIqb7rxHqQIqkpZiSreYkiMcITNCJ9QyPEiRqkxTcyeGqUIQyFNC/SsFD/dqSIKzXlgaksjl70cvE/r5/o8GqQ0ihONInwbFGYMKgFzDOBQyoJ1mxqCMKSmlshHiOJsDbJzW3JZ0sVqqxmonEXg1gmnfOG6zTc+4t687oMqQqOwAk4Ay64BE1wC1qgDTB4Ai/gFbxZz9a79WF9zkorVtlzCOZgff0CLDWikw==</latexit>
L1 = first-order logic<latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit><latexit sha1_base64="45ddNPsZu/fZxPjqZFRqcoCgy/Q=">AAACJ3icbVDLSsNAFJ34rPUVdelmsAjdWBIRdCMU3bhwUcE+oAlhMp20QyeZMDMRS8gv+B/u3eovuBNduvMznKRZ2NYDA4dz7muOHzMqlWV9GUvLK6tr65WN6ubW9s6uubffkTwRmLQxZ1z0fCQJoxFpK6oY6cWCoNBnpOuPr3O/+0CEpDy6V5OYuCEaRjSgGCkteWbdCZEaSSzS28yz4SV0Qp8/pgEVUp1wMSACMj6kOPPMmtWwCsBFYpekBkq0PPPHGXCchCRSmCEp+7YVKzdFQlHMSFZ1EklihMdoSPqaRigk0k2LH2XwWCsDGHChX6Rgof7tSFEo5ST0dWVx/7yXi/95/UQFF25KozhRJMLTRUHCoOIwjwcOqCBYsYkmCAuqb4V4hATCSoc4syWfLWQgs6qOxp4PYpF0Thu21bDvzmrNqzKkCjgER6AObHAOmuAGtEAbYPAEXsAreDOejXfjw/icli4ZZc8BmIHx/QuIhqbm</latexit>
L0 = zeroth-order logic<latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit><latexit sha1_base64="rae+VGvksk3nCsYockaB25wnhnQ=">AAACKHicbVDLSsNAFJ3UV62vqks3g0XQhSURQTdC0Y0LFxXsA9pSJtObdugkE2YmYg35Bv/DvVv9BXfSrSs/w0mbhW09MHA45z7mHjfkTGnbHlu5peWV1bX8emFjc2t7p7i7V1cikhRqVHAhmy5RwFkANc00h2Yogfguh4Y7vEn9xiNIxUTwoEchdHzSD5jHKNFG6hZP2j7RA0VlfJd0bXyF274rnuJnkEIPToXsgcRc9BlNusWSXbYnwIvEyUgJZah2iz/tnqCRD4GmnCjVcuxQd2IiNaMckkI7UhASOiR9aBkaEB9UJ56clOAjo/SwJ6R5gcYT9W9HTHylRr5rKicHzHup+J/XirR32YlZEEYaAjpd5EUca4HTfHCPSaCajwwhVDLzV0wHRBKqTYozW9LZUnkqKZhonPkgFkn9rOzYZef+vFS5zkLKowN0iI6Rgy5QBd2iKqohil7QG3pHH9ar9Wl9WeNpac7KevbRDKzvX3aSp2M=</latexit>
LPropCalc = propositional calculus<latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit><latexit sha1_base64="DE1nAlInoZB4QbARKY9i/o//6a4=">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</latexit>
DCEC⇤<latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit><latexit sha1_base64="jH7bxOPxNLvK9MqLWOo6fnj1hGk=">AAACEnicbVDLSsNAFJ3UV62vaJduBovgqiQi6LJYBZcV7AOaWG6mk3bo5MHMRCghf+Herf6CO3HrD/gHfoaTNgvbemDgcM69cw/HizmTyrK+jdLa+sbmVnm7srO7t39gHh51ZJQIQtsk4pHoeSApZyFtK6Y47cWCQuBx2vUmzdzvPlEhWRQ+qGlM3QBGIfMZAaWlgVl1AlBjAjy9ad42s0cHpBqYNatuzYBXiV2QGirQGpg/zjAiSUBDRThI2betWLkpCMUIp1nFSSSNgUxgRPuahhBQ6aaz8Bk+1coQ+5HQL1R4pv7dSCGQchp4ejKPKpe9XPzP6yfKv3JTFsaJoiGZH/ITjlWE8ybwkAlKFJ9qAkQwnRWTMQggSve1cCX/W0hfZhVdjb1cxCrpnNdtq27fX9Qa10VJZXSMTtAZstElaqA71EJtRNAUvaBX9GY8G+/Gh/E5Hy0ZxU4VLcD4+gWz5p4L</latexit>
The Physical Universe
Non-Physical
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modus ponens
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Page 47
Next problem(King-Ace) …
Page 48
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
Page 49
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.
Page 50
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.
Page 51
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.NO!
Page 52
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
Page 53
The Original King-AceSuppose that the following premise is true:
If there is a king in the hand, then there is an acein the hand, or else if there isn’t a king in the hand,then there is an ace.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Page 54
King-Ace Solved
Proposition: There is not an ace in the hand.
Proof: We know that at least one of the if-thens (i.e., at least one of the conditionals) is false. So we have two cases to consider, viz., that K => A is false, and that ¬K => A is false. Take first the first case; accordingly, suppose that K => A is false. Then it follows that K is true (since when a conditional is false, its antecedent holds but its consequent doesn’t), and A is false. Now consider the second case, which consists in ¬K => A being false. Here, in a direct parallel, we know ¬K and, once again, ¬A. In both of our two cases, which are exhaustive, there is no ace in the hand. The proposition is established. QED
Page 55
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
Page 56
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.
Page 57
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.
Page 58
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO!
Page 59
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
Page 60
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Page 61
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Page 62
Study the S-expression
Page 63
Study the S-expression
Page 64
We need another rule of inference to crack this problem … …
Page 65
We need another rule of inference to crack this problem … …
disjunction elimination
Page 66
From ~ p. 54 in LAMA-BDLA
Page 67
From ~ p. 54 in LAMA-BDLA
Page 68
From ~ p. 54 in LAMA-BDLA
Page 69
From ~ p. 54 in LAMA-BDLA
?
Page 70
From ~ p. 54 in LAMA-BDLA
?
Page 71
From ~ p. 54 in LAMA-BDLA
?
Page 72
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Page 73
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Page 74
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Page 75
King-Ace 2Suppose that the following premise is true:
If there is a king in the hand, then there is an ace in the hand; or if there isn’t a king in the hand, then there is an ace; but not both of these if-then statements are true.
What can you infer from this premise?
There is an ace in the hand.NO! NO!
In fact, what you can infer is that there isn’t an ace in the hand!
Exercise (on HyperGraderTM): Finish the proof in HyperSlateTM — with no remaining use of an oracle.