OTTER;Suppositional Theorem-Proving and OSCAR;

Automated Test Creation and Production2/12/01

Logic (Programming) & AISelmer Bringsjord

selmer@rpi.edu

www.rpi.edu/~brings

General discussion of LP paradigm…

Recall: Two Perspectives

• Logic Programming as arising from Herbrand’s Theorem, etc.

• Logic Programming as using a logical system (in mathematical sense of this phrase)

• I will take second perspective, which subsumes first– E.g., completeness theorem for first-order logic (LI)

allows one to affirm Herbrand’s Theorem– This theorem fully done in LCU

• What you need to know to understand second perspective is precisely what you need to know to understand first

The Dreadsbury Mansion MysterySomeone who lives in Dreadsbury Mansion killed Aunt Agatha. Agatha, the butler, and Charles live in Dreadsbury Mansion, and are the only people who live therein. A killer always hates his victim, and is never richer than his victim. Charles hates no one that Aunt Agatha hates. Agatha hates everyone except the butler. The butler hates everyone not richer than Aunt Agatha. The butler hates everyone Agatha hates. No one hates everyone. Agatha is not the butler.

Now, given the above clues, there is a bit of disagreementbetween three (competent?) Norwegian detectives. Inspector Bjorn is sure that Charles didn’t do it. Is he right? Inspector Reidar is sure that it was a suicide. Is he right? Inspector Olaf is sure that the butler, despite conventional wisdom, is innocent. Is he right?

Can you get it, prove it?

On OTTER

• Return to Logic Theorist problems• Syllogisms in OTTER• LCU and resolution rules. Also in AIMA• Jobs puzzle and other things online…• Dreadsbury Mansion Mystery in OTTER

– My first exercise

• “Victor” Murder Mystery in OTTER• Bird problem in OTTER (unilluminating)

Overview of OSCAR in Connection to Natural

Deduction…

first via “Bird” Problem in Hyperproof, then

via Pollock’s ppt file…

The Bird Problem

Is the following assertion true or false? Prove that you are correct.

There exists something which is such that if it’s a bird, theneverything is a bird.

x(B(x) yB(y))

Good litmus test for mastery of proof theory in FOL

Overview of Intelligent Test

Creation/Production…other ppt file