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LOGIC behind Technologies THE presented by Apinya Dhatsuwan
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Page 1: Logic behind technology

LOGICbehind

Technologies

THE

presented by Apinya Dhatsuwan

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STUDY OF LOGIC

Mathematics

Philosophy

Semantics

Computer science

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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

http://www.graphicsfactory.com/clip-art/image_files/tn_image/7/727607-tn_working_069-c.jpghttp://us.cdn2.123rf.com/168nwm/artefy/artefy1103/artefy110300014/9216244-white-woman-dressed-like-old-fashioned-french-cook-is-smiling-with-a-spoon-in-her-hand.jpg

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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)

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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