Logic behind technology


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  • First of all, ARISTOTLE , he talked about the Laws of Logical Thought which is the starting point of the Logic.
  • This is an Apple (If) this a fresh apple.This cannot be both fresh apple and rot apple in the same timeAnd this apple is fresh apple is True
  • Logic was established as a discipline by Aristotle, who gave it a fundamental place in philosophy.He asserted that “…”
  • A All S are P universal affirmatives All humans are mortal.E No S are P universal negatives No humans are perfect.I Some S are P particular affirmatives Some humans are healthy.O Some S are not P particular negatives Some humans are not clever.(ใช้ตัวสีแดง เพื่อให้ได้รู้ว่า a, e, I,oคือ อะไร)มีข้อสงสัยว่า เมื่อ s แทน humans ในทุกๆ type แล้ว ทำไม p ในแต่ละ type ถึงไม่เหมือนกันคะ?????
  • George Boole Born in the English industrial town of LincolnHis parents were Mary Ann Joyce and John Boole. John made shoes & Mary Ann was a lady's maid.Boole was lucky enough to have a father who interested in science and in particular the application of mathematics to scientific instruments. Young George took to learning like a politician to a pay rise and, by the age of eight, had outgrown his father's self-taught limits. >>growing up to be a mathematical genius
  • 1844 he was concentrating on the uses of combined algebra and calculus to process infinitely small and large figures,It was published by Boole in the “Transactions of the Royal Society”.In the same year, he received the Society's Royal Medal 1854 Boole's published his most important work“An investigation into the Laws of Thought of Aristotle, on Which are founded the Mathematical Theories of Logic and Probabilities”
  • http://www.allaboutcircuits.com/vol_4/chpt_7/2.htmlHe codified several rules of relationship between mathematical quantities limited to one of two possible values:true or false, 1 or 0.It should be clearly understood that Boolean numbers are not the same as binary numbers. Whereas Boolean numbers represent an entirely different system of mathematics from real numbers, binary is nothing more than an alternative notation for real numbers. The two are often confused because both Boolean math and binary notation use the same two ciphers: 1 and 0. The 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. The binary number 100112 ("nineteen") has no more place in the Boolean world than the decimal number 210 ("two") or the octal number 328 ("twenty-six").There are three common Boolean operatorsMost search tools offer some type of Boolean search option as a way of constructing your search, and indicating the relationships between your search terms.
  • The first three sums make perfect sense to anyone familiar with elementary addition. The last sum, though, is quite possibly responsible for more confusion than any other single statement in digital electronics, because it seems to run contrary to the basic principles of mathematics. Well, it does contradict principles of addition for real numbers, but not for Boolean numbers. Remember that in the world of Boolean algebra, there are only two possible values for any quantity and for any arithmetic operation: 1 or 0. There is no such thing as "2" within the scope of Boolean values. Since the sum "1 + 1" certainly isn't 0, it must be 1 by process of elimination.
  • Logic behind technology

    1. 1. LOGIC presented by Apinya Dhatsuwan
    2. 2. STUDY OF LOGIC Mathematics Philosophy Semantics Computer science 2
    3. 3. http://www.cheniere.org/books/aids/appendixIII.htm Laws of Logical Thought • law of identity Thing is the same as itself • law of non- contradiction Nothing can both be and not be • law of excluded middle Everything is either be ARISTOTLE (384 BC – 322 BC) 3
    4. 4. 4 ARISTOTLE (384 BC – 322 BC)
    5. 5. http://g-ecx.images-amazon.com/images/G/01/askville/5481910_9029237_mywrite/aristotle.gif …it will not be possible to be and not to be the same thing 5
    6. 6. 6 ARISTOTLE (384 BC – 322 BC)
    7. 7. 7 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 himself at risk for diabetes ARISTOTLE (384 BC – 322 BC)
    8. 8. 8 The propositions of a syllogism can be any of 4 types S = Subject of Conclusion P = Predicate of Conclusion SaP All S are P All humans are mortal SeP No S are P No humans are perfect SiP Some S are P Some humans are healthy SoP Some S are not P Some humans are not clever ARISTOTLE (384 BC – 322 BC)
    9. 9. 99 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)
    10. 10. 1815 Lincoln, England http://www.graphicsfactory.com/clip-art/image_files/tn_image/7/727607-tn_working_069-c.jpg http://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 10
    11. 11. His methods were outlined in two major works, The Mathematical Analysis of Logic (1847) and An Investigation into the Laws of Thought (1854) 11 GEORGE BOOLE (1815 - 1864)
    12. 12. http://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 12 GEORGE BOOLE (1815 - 1864) Boolean algebra Relationship between two possible values: true or false, 1 or 0 Boolean numbers are not the same as binary numbers Both Boolean math and binary notation use the same two ciphers: 1 and 0 The 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:
    13. 13. 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 AND is represented as multiplication OR is represented as addition Not is represented as complement or negation 0 X 0 = 0 0 X 1 = 0 1 X 0 = 0 1 X 1 = 1 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 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 13 GEORGE BOOLE (1815 - 1864) the opposite of its value
    14. 14. 14 The Father Of The Digital Computer invented the first automatic electronic digital computer John Vincent Atanasoff (19
    15. 15. John Vincent Atanasoff (19 1903 Hamilton, New York Senior Electrical EngineerMathematics School Teacher 15
    16. 16. John Vincent Atanasoff (19 Monroe calculator Clifford E. BerryJohn Atanasoff Associate-professor in physics and mathematics 16
    17. 17. 17 John Vincent Atanasoff (19 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.
    18. 18. John Vincent Atanasoff (19 Atanasoff-Berry Computer: ABC 18 • 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 logic Computations would be done by what Atanasoff termed “direct logical action”
    19. 19. Lotfali Askar Zadeh (1921) American, Russian, Iranian, Azerbaijani Mathematician, Electrical Engineer, Computer Scientist and Professor of Computer Science 19
    20. 20. Lotfali Askar Zadeh (1921) 20 Qualita tive Subjecti ve http://www.maycomplicateeverything.com/files/gimgs/8_oven.png Real world is very complex Qualitative Measure
    21. 21. 21
    22. 22. 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 Soft unsharp blurred elastic Fuzzyrejects the law of the excluded middle and allows as a truth value any real number between 0 and 1 22
    23. 23. 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 23
    24. 24. 24 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
    25. 25. 25 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 conditions microprocessors store and process fuzzy rules
    26. 26. 26 Output:motorspeed 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)
    27. 27. Use of Fuzzy Logic 27
    28. 28. 28 Special Thanks Patcharin Panjaburee,
    29. 29. 29
    30. 30. 30 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
    31. 31. 31 John Vincent Atanasoff (19 Atanasoff did not recognize the application of Boolean algebra to his problem He devised his own direct logical action by trial and error He was unaware that in 1938, Claude Shannon proved that two-valued Boolean algebra could describe the operation of two-valued electrical Claude Shannon