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Lecture 15 of 42. First-Order Logic: Resolution Discussion: AI Applications 2 of 3. Wednesday, 27 September 2007 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: http://snipurl.com/v9v3 - PowerPoint PPT Presentation
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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