# Lecture Notes for CS 440 - Artificial Intelligence at Illinois (UIUC)

## Notes Information

 Material Type: Class Note Professor: Staff Class: CS 440 - Artificial Intelligence Subject: Computer Science University: University of Illinois - Urbana-Champaign Term: Spring 2006 Keywords: Binding ListContradictionSubstitutionGeneralizedComplicationsConjunctiveStandardizeConjunctionEliminationForward Chaining

## Sample Document Text

Inference in First Order Logic Introduction to Artificial Intelligence CS440/ECE448 Lecture 12 New homework out today, due March 2 Last lecture . Examples of sentences . Simple inference rules . Inference with quantifiers This lecture . Substitutions and unification . Generalized Modus Ponens . Resolution and refutation Reading . Chapter 9 Substitutions Given a sentence ? and binding list ?, the result of applying the substitution ? to ? is denoted by Subst(?, ?). Example: ? = {x/Sam, y/Pam} ? = Likes(x,y) Subst({x/Sam, y/Pam}, Likes(x,y)) = Likes(Sam, Pam) Universal Elimination (UE): ? x ? Subst({x/?}, ?) [? must be a ground term (i.e., no variables).] Example Imagine Universe of Discourse is {Rodrigo, Sharon, David, Jonathan} ? x At (x, UIUC) ? OK(x) At(Rodrigo, UIUC) ? OK(Rodrigo) Inference with Universal Quantifiers substitution list Inference with Existential Quantifiers Existential Elimination: ?? ? Subst({?/k}, ? ) where k is a new (Skolem) constant. Example Fro...

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