Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Lecture 15 of 42

Wednesday, 27 September 2007

William H. Hsu

Department of Computing and Information Sciences, KSU

KSOL course page: http://snipurl.com/v9v3

Course web site: http://www.kddresearch.org/Courses/Fall-2007/CIS730

Instructor home page: http://www.cis.ksu.edu/~bhsu

Reading for Next Class:

Section 9.5 – 9.6, p. 295 - 310, Russell & Norvig 2nd edition

First-Order Logic: ResolutionDiscussion: AI Applications 2 of 3

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Lecture Outline

Reading for Next Class: Section 9.5 – 9.6, R&N 2e

Today Resolution theorem proving

Prolog as related to resolution

Decidability of SAT, VALID

Recursive, Recursive Enumerable, and Co-RE languages

MP4 & 5 preparations

Friday Logic programming in real life

Industrial-strength Prolog

Lead-in to MP4

Next Week

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides byS. Russell, UC Berkeley

Logical Agents:Review

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Example:Backward Chaining

Adapted from slides byS. Russell, UC Berkeley

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Question: How Does This Relate to Proof by Refutation?

Answer Suppose ¬Query, For The Sake Of Contradiction (FTSOC)

Attempt to prove that KB ¬Query ⊢

Backward Chaining

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Resolution Inference Rule

Adapted from slides byS. Russell, UC Berkeley

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

Conjunctive Normal (aka Clausal) Form:Conversion (Nilsson) and Mnemonic

Implications Out

Negations Out

Standardize Variables Apart

Existentials Out (Skolemize)

Universals Made Implicit

Distribute And Over Or (i.e., Disjunctions In)

Operators Out

Rename Variables

A Memonic for Star Trek: The Next Generation Fans

•Captain Picard:

•I’ll Notify Spock’s Eminent Underground Dissidents On Romulus

•I’ll Notify Sarek’s Eminent Underground Descendant On Romulus

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

Skolemization

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

Resolution Theorem Proving

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

Example:Resolution Proof

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Offline Exercise:Read-and-Explain Pairs

Offline Exercise:Read-and-Explain Pairs

For Class Participation (PS5) With Your Assigned Partner(s)

Read: Chapter 10 R&N By 13 Oct 2007

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

Logic Programming vs. Imperative Programming

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

A Look Ahead:Logic Programming as Horn Clause

Resolution

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Adapted from slides by S. Russell, UC Berkeley

A Look Ahead:Logic Programming (Prolog) Examples

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Summary Points

From Propositional to First-Order Proofs Generalized Modus Ponens

Resolution

Unification Problem

Roles in Computer Science Type inference

Theorem proving

What do these have to do with each other?

Search Patterns Forward chaining

Backward chaining

Fan-in, fan-out

Computing & Information SciencesKansas State University

Wednesday. 26 Sep 2007CIS 530 / 730: Artificial Intelligence

Terminology

From Propositional to First-Order Proofs Generalized Modus Ponens

Resolution

Unification Problem

Most General Unifier (MGU)

Roles in Computer Science Type inference

Theorem proving

What do these have to do with each other?

Search Patterns Forward chaining

Backward chaining

Fan-in, fan-out