LOGIC behind Technologies THE presented by Apinya Dhatsuwan
Oct 31, 2014
LOGICbehind
Technologies
THE
presented by Apinya Dhatsuwan
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STUDY OF LOGIC
Mathematics
Philosophy
Semantics
Computer science
3http://www.cheniere.org/books/aids/appendixIII.htm
Laws of Logical Thought• law of identity
Thing is the same as itself
• law of non-contradictionNothing can both be and not be
• law of excluded middleEverything is either be or not be
ARISTOTLE (384 BC – 322 BC)
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ARISTOTLE (384 BC – 322 BC)
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…it will not be
possible to be and not to be the same
thing
“
”
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ARISTOTLE (384 BC – 322 BC)
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The parts of syllogistic logic, also known by the name term logic, are the analysis of the judgments into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consist of two propositions sharing a common term as premise, and a conclusion which is a proposition involving the two unrelated terms from the premises.
Major premise: Eating sweets every day,is placing yourself at risk for diabetes.
Minor premise: John eat sweats everyday
Conclusion: Therefore John is placing himselfat risk for diabetes
ARISTOTLE (384 BC – 322 BC)
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The propositions of a syllogism can be any of 4 typesS = Subject of ConclusionP = Predicate of Conclusion
SaP All S are P All humans are mortalSeP No S are P No humans are perfectSiP Some S are P Some humans are healthySoP Some S are not P Some humans are not clever
ARISTOTLE (384 BC – 322 BC)
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English mathematician and a founder of the algebraic tradition in logic
• He revolutionized logic by
applying methods from symbolic
algebra to logic.
• Traditional (Aristotelian) logic
relied on cataloging the valid
syllogisms of various simple
forms.
• Boole sought to give symbolic
form to Aristotle's system of
logic.
GEORGE BOOLE (1815 - 1864)
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1815 Lincoln, England
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His methods were outlined in two major works, The Mathematical Analysis of Logic (1847) and An Investigation into the Laws of Thought (1854)
GEORGE BOOLE (1815 - 1864)
12http://www.sciencephoto.com/image/223560/large/H4020347-George_Boole-SPL.jpg
An investigation into the Laws of Thought,on Which are founded the Mathematical Theories of Logic and Probabilities
AND OR NOT
GEORGE BOOLE (1815 - 1864)
Boolean algebraRelationship between two possible values: true or false, 1 or 0 Boolean numbers are not the same as binary numbersBoth Boolean math and binary notation use the same two ciphers: 1 and 0The difference is that Boolean quantities are restricted to a single bit (either 1 or 0), whereas binary numbers may be composed of many bits adding up in place-weighted form to a value of any finite size
Operators:
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OR 0 1
0 0 1
1 1 1
AND 0 1
0 0 0
1 0 1
NOT 0 1
1 0
AND is represented as multiplicationOR is represented as additionNot is represented as complement or negation
0 X 0 = 00 X 1 = 01 X 0 = 01 X 1 = 1
0 + 0 = 00 + 1 = 11 + 0 = 11 + 1 = 1
In the world of Boolean algebra, there are only two possible values for any quantity and for any arithmetic operation: 1 or 0
GEORGE BOOLE (1815 - 1864)
the opposite of its value
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The Father Of The Digital Computerinvented the first automatic electronic digital computer
John Vincent Atanasoff (1903 – 1995)
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John Vincent Atanasoff (1903 – 1995)
1903 Hamilton, New York
Senior Electrical EngineerMathematics School Teacher
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John Vincent Atanasoff (1903 – 1995)
Monroe calculator
Clifford E. BerryJohn Atanasoff
Associate-professor in physics and mathematics
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John Vincent Atanasoff (1903 – 1995)
His machine would have to be electronic-the mathematical operations would occur by
changes in electrical charges rather than mechanical
movements
Use digital, system with base two, or binary, mathematics that would ensure precision and be compatible with the on-off nature of electronics.
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John Vincent Atanasoff (1903 – 1995)
Atanasoff-Berry Computer: ABC
• Binary system, Boolean logic and a regenerative capacitor memory
• Designed to solve up to 29 linear equations
• Had no CPU, but using vacuum tubes for digital computation, used punched cards for input
Computability logic is opposed to classical logicComputations would be done by what Atanasoff termed “direct logical action”
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Lotfali Askar Zadeh (1921)
American, Russian, Iranian, AzerbaijaniMathematician, Electrical Engineer, Computer Scientist and Professor of Computer Science
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Lotfali Askar Zadeh (1921)
Qualitative
Subjective
http://www.maycomplicateeverything.com/files/gimgs/8_oven.png
Real world is very complex
Qualitative Measure
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Lotfali Askar Zadeh (1921)
The law of the excluded middle p or ~p must be true. no middle true proposition between them Aristotle’s day: precise as possible
Softunsharp
blurred
elastic
Fuzzyrejects the law of the excluded middle and allows as a truth value any real
number between 0 and 1
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Lotfali Askar Zadeh (1921)
Fuzzy Logic = Computing with Word
The basis for fuzzy logic is the basis for human communication. Because
fuzzy logic is built on the structures of qualitative
description used in everyday language.
Fuzzy logic is designed to solve
problems in the same way that
humans do
Machines can be programmed
to process approximate
data and deal with the gray areas of life.Fuzzy logic's approach to control
problems mimics how a person would make decisions, only much faster.
Real world is very complex
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Lotfali Askar Zadeh (1921)
http://upload.wikimedia.org/wikipedia/commons/thumb/6/61/Fuzzy_logic_temperature_en.svg/1000px-Fuzzy_logic_temperature_en.svg.png
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Lotfali Askar Zadeh (1921)How fast they should shift from one setting to another
"If the temperature is cool, then set the motor speed on slow" "If the temperature is just right, then set the motor speed on medium."
IF...THEN convert inputs to outputs-one fuzzy set into another
Temperature sets (cold, cool, just right, warm and hot)
Motor speed sets (very slow , slow , medium, fast and very fast)
Fuzzy Inputs
Fuzzy Outputs
sensors measure changing input conditionsmicroprocessors store and process fuzzy rules
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Out
put :
mot
or s
peed
Input : temperature sets
Cold Cool Just Right Warm Hot
Very Fast
Fast
Medium
Slow
Very Slow
IF Warm THEN Fast
IF Just Right THEN Medium
IF Cool THEN Slow
Lotfali Askar Zadeh (1921)
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Use of Fuzzy Logic
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Special Thanks
Patcharin Panjaburee, PhD.
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Thank you
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Subtraction implies the existence of negative numbers: 5 - 3 is the same thing as 5 + (-3), and in Boolean algebra negative quantities are forbidden. There is no such thing as division in Boolean mathematics, either, since division is really nothing more than compounded subtraction.
GEORGE BOOLE (1815 - 1864)
To calculate the 2's complement of an integer, invert the binary equivalent of the number by changing all of the ones to zeroes and all of the zeroes to ones (also called 1's complement), and then add one.
For example,
0001 0001(binary 17) 1110 1111(two's complement -17) NOT(0001 0001) = 1110 1110 (Invert bits)1110 1110 + 0000 0001 = 1110 1111 (Add 1)
The most significant (leftmost) bit indicates the sign of the integer; therefore it is sometimes called the sign bit.If the sign bit is zero, then the number is greater than or equal to zero, or positive.If the sign bit is one, then the number is less than zero, or negative.
2's Complement
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John Vincent Atanasoff (1903 – 1995)
Atanasoff did not recognize the application of Boolean algebra to his problem He devised his own direct logical action by trial and errorHe was unaware that in 1938, Claude Shannon proved that two-valued Boolean algebra could describe the operation of two-valued electrical switching circuits.
Claude Shannon