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History of IT and AI 1/8/01 Logic (Programming) & AI Selmer Bringsjord selmer@rpi.edu www.rpi.edu/~brings

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What is a Proof? Aristotle –Syllogisms –Frenchmen example… –Fatal problems (including can’t handle Euclid!) If Jason is in fact a financial whiz, then the Giants will win the Superbowl. Jason is in fact a financial whiz. Therefore the Giants will win the Superbowl. Minor enhancements from Stoics and Medievil logicians –E.g., modus ponens… –But 2,400 yrs until real progress!

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Story Continues Lull and his wheel (14 th century) –Check out the cover of AIMA: there’s a lot there Hobbes: “Thinking is calculation” (17 th century) DesCartes: Deduction is the method; linguistic capacity the human/animal divide –(By Selmer’s lights, DesCartes seems to have gotten things essentialy correct) And suddenly Boole appears!

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Boole’s Innovation Essentially the Propositional Calculus p, q, r, … Boolean connective Approximate English correlate Not And Or If …, then … … if and only if …

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Frege Answers the Question! First-order Logic Add –variables x, y, z, … –quantifiers –relation symbols R, F, G, … “Everyone loves someone” is x yLxy A proof is reasoning that can be formalized as a step-by-step progression in first-order logic…

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And Shortly Thereafter… Kronecker refuses to accept Cantor’s Proof –E.g., that the power set of the natural numbers is “larger” than the natural numbers Hilbert expresses Kronecker’s attitude in his “program”: use algorithms to answer all mathematical questions Gödel obliterates Hilbert’s dream; Turing follows suit (and actually generalizes, with a simpler proof) Gödel needs precise account of computable Turing provides “Turing Machines” –Out of TMs we get digital computers –Turing not sure a physical UTM is physically possible! Church: “Hey, TMs, -calculus, etc. all the same!”

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Intuitive Picture of Turing Machine

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And AI and Agent Tech Specifically? Artificial Neurons: McCulloch & Pitts –Prop. Calc. + Turing Machines + Neurophysiology Princeton –Minsky: Neural networks –McCarthy there as well Dartmouth workshop 1956 –Minsky, McCarthy, Simon, Newell, … –Logic Theorist!

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And… McCarthy in 1958 –Lisp born –Advice Taker –McCarthy and Minsky clash over logic –McCarthy leaves for Stanford Minsky and Microworlds Minsky and Pappert kill connectionist approach Logicist systems rule (expert systems) Connectionism comes back And today? –New edition of AIMA reacts to Web –Hybrid approaches –,,,

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