IST4_lec7

IST4_lec7 - IST 4 Information and Logic IST 4: Planned...

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IST 4 Information and Logic
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1 M1 31 6 2 6 5 26 19 M2 5 4 12 4 5 3 M2 28 3 2 21 2 1 14 M1 7 fri thr wed tue mon IST 4: Planned Schedule – Spring 2008 x= hw#x out x= hw#x due = today T Mx= MQx out Mx= MQx due midterms midterms T
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From Natural Sense to Syntax to Algebra logical sense number sense one-to-one counting number system physical composition abstract composition - syntax boxes small syntax boxes algebra for syntax composition one-to-one classification limited abstract composition general composition dream physical composition word system single words language
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A Magic Box a b a b m 0 0 1 0 1 0 1 1 1 1 1 0 A binary s-box that can compute any binary s-box ? m
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Algorithms – Syntax Manipulation 2 symbol adder c s d1 d2 c 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 a b 0 0 1 0 1 0 1 1 o 0 0 0 1 a b 0 0 1 0 1 0 1 1 o 0 1 1 1
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a b a b m 0 0 1 0 1 0 1 1 1 1 1 0 a b 0 0 1 0 1 0 1 1 o 0 0 0 1 o 1 0 1 0 0 0 1 0 0 Magic Box for Arithmetic
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Magic Box for Arithmetic a a b m 0 0 1 0 1 0 1 1 1 1 1 0 a b 0 0 1 0 1 0 1 1 o 0 1 1 1 o b 1 1 1 1 0 0 1 0 1
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How will you find the composition? A Magic Box a b m 0 0 1 0 1 0 1 1 1 1 1 0 A binary s-box that can compute any binary s-box ? o How will you prove that? We need a Language for s-boxes!! Maybe Boolean Algebra??
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Aristotle 384-322 BC Aristotle key motivation for developing logic was to provide a procedure for checking the validity of arguments and to derive new conclusions based on existing premises Aristotle and Logic A syllogism (Greek: "conclusion", "inference"), a categorical syllogism, is a kind of logical argument in which one proposition ( the conclusion ) is inferred from two others ( the premises ) of a certain form •No ±homework± is ±fun • IST4 assignments are homework • IST4 should not have assignments, A+ for everyone!
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•The Babylonians were wise people •Le ibn iz±was ±a ±w ise ±person • Leibniz was a Babylonian Aristotle and Logic
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• People that are wise are Babylonians •Le ibn iz±was ±w ise • Leibniz was a Babylonian Aristotle and Logic
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Lewis on Syllogism The logical sense = number sense = 3 We need a “number system” for logic to extend our “logical sense”
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Syllogism to Algebra George Boole, 1847 George Boole 1815 –1864
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Syllogism to Algebra George Boole, 1847 Algebra of classes
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This note was uploaded on 12/12/2009 for the course IST 4 taught by Professor Shuki during the Spring '09 term at Caltech.

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IST4_lec7 - IST 4 Information and Logic IST 4: Planned...

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