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History of IT and AI 1/8/01. Logic (Programming) & AI Selmer Bringsjord [email protected] www.rpi.edu/~brings. What is a Proof?. Aristotle Syllogisms Frenchmen example… Fatal problems (including can’t handle Euclid!)

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History of it and ai 1 8 01 l.jpg

History of IT and AI1/8/01

Logic (Programming) & AI

Selmer Bringsjord

[email protected]

www.rpi.edu/~brings


What is a proof l.jpg
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!


Story continues l.jpg
Story Continues

  • Lull and his wheel (14th century)

    • Check out the cover of AIMA: there’s a lot there

  • Hobbes: “Thinking is calculation” (17th 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!


Boole s innovation essentially the propositional calculus l.jpg
Boole’s Innovation Essentiallythe Propositional Calculus

  • p, q, r, …


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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!”



And ai and agent tech specifically l.jpg
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!


Slide9 l.jpg
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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