computing & information sciences kansas state university lecture 12 of 42 cis 530 / 730...
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence © 2004 S. Russell & P. Norvig. Reused with permission. Chapter 7 ConcludedTRANSCRIPT
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Lecture 12 of 42
William H. HsuDepartment of Computing and Information Sciences, KSU
KSOL course page: http://snipurl.com/v9v3Course web site: http://www.kddresearch.org/Courses/CIS730
Instructor home page: http://www.cis.ksu.edu/~bhsu
Reading for Next Class:
Section 8.3 – 8.4, p. 253 - 266, Russell & Norvig 2nd editionHandout, Nilsson & Genesereth, Logical Foundations of Artificial Intelligence
Intro to First-Order Logic:Syntax and Semantics
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Lecture Outline Reading for Next Class: 8.3-8.4 (p. 253-266), 9.1 (p. 272-274), R&N 2e
Last Class: Propositional Logic, Sections 7.5-7.7 (p. 211-232), R&N 2e
Properties of sentences (and sets of sentences, aka knowledge bases)entailmentprovability/derivabilityvalidity: truth in all models (aka tautological truth)satisfiability: truth in some models
Properties of proof rulessoundness: KB ⊢i α KB ⊨ α (can prove only true sentences)completeness: KB ⊨ α KB ⊢ i α (can prove all true sentences)
Still to Cover in Chapter 7: Resolution, Conjunctive Normal Form (CNF) Today: Intro to First-Order Logic, Sections 8.1-8.2 (p. 240-253), R&N 2e
Elements of logic: ontology and epistemology Resolution theorem proving First-order predicate calculus (FOPC) aka first order logic (FOL)
Coming Week: Propositional and First-Order Logic (Ch. 8 – 9)
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
© 2004 S. Russell & P. Norvig. Reused with permission.
Chapter 7Concluded
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
© 2004 S. Russell & P. Norvig. Reused with permission.
Inference:Review
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
© 2004 S. Russell & P. Norvig. Reused with permission.
Validity and Satisfiability:Review
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Forward Chaining Example:Review
Adapted from slides © 2004 S. Russell & P. Norvig. Reused with permission.
2 2
2
2
1 n: number of antecedents (LHS conjuncts) still unmatched
1 1
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1
1 0
1
2
1
1 0
0
1
1
1 0
0
0
1
0 0
0
0
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0 0
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0
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Backward Chaining Example:Review
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Forward vs. Backward Chaining:Review
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Resolution [1]:Propositional Sequent Rule
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Resolution [2]: Conversion to Conjunctive Normal Form (CNF)
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Resolution [3]:Algorithm
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Resolution [4]:Example
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Chapter 7:Summary
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Chapter 8: Overview
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Propositional Logic:Pros and Cons
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
First-Order Logic (FOL)
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Logics in General:Ontological and Epistemic Aspects
Adapted from slide © 2004 S. Russell & P. Norvig. Reused with permission.
Ontological commitment – what entities, relationships, and facts exist in world and can be reasoned about
Epistemic commitment – what agents can know about the world
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Syntax of FOL:Basic Elements
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Atomic Sentences(aka Atoms, aka Atomic WFFs)
Adapted from slide © 2004 S. Russell & P. Norvig. Reused with permission.
Atomic sentence – smallest unit of a logic (aka “atom”, “atomic well-formed formula (atomic WFF)”
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Complex Sentences
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Truth in First-Order Logic
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Models for FOL:Example
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Models for FOL:Example
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Models for FOL:Lots!
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Universal Quantification [1]:Definition
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Universal Quantification [2]:Common Mistake to Avoid
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Existential Quantification [1]:Definition
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Existential Quantification [2]:Common Mistake to Avoid
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Properties of Quantifiers
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Fun With Sentences
Adapted from slides © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Equality
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Interacting with FOL KBs
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Knowledge Base forWumpus World
Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Deducing Hidden Properties
© 2004 S. Russell & P. Norvig. Reused with permission.
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Terminology First-Order Logic (FOL) aka First-Order Predicate Calculus (FOPC)
ComponentsSemantics (meaning, denotation): objects, functions, relationsSyntax: constants, variables, terms, predicates
Properties of sentences (and sets of sentences, aka knowledge bases)entailmentprovability/derivabilityvalidity: truth in all models (aka tautological truth)satisfiability: truth in some models
Properties of proof rulessoundness: KB ⊢i α KB ⊨ α (can prove only true sentences)completeness: KB ⊨ α KB ⊢ i α (can prove all true sentences)
Conjunctive Normal Form (CNF) Universal Quantification (“For All”) Existential Quantification (“Exists”)
Computing & Information SciencesKansas State University
Lecture 12 of 42CIS 530 / 730Artificial Intelligence
Last Class: Overview of Knowledge Representation (KR) and Logic Representations covered in this course, by ontology and epistemology Propositional calculus (aka propositional logic)
Syntax and semanticsRelationship to Boolean algebraProperties
Propositional Resolution Elements of Logics – Ontology, Epistemology Today: First-Order Logic (FOL) aka FOPC
Components: syntax, semantics Sentences: entailment vs. provability/derivability, validity vs. satisfiability Soundness and completeness Properties of proof rules
soundness: KB ⊢i α KB ⊨ α (can prove only true sentences)completeness: KB ⊨ α KB ⊢ i α (can prove all true sentences)
Next: First-Order Resolution
Summary Points