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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Lecture 12 of 42 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: http://snipurl.com/v9v3http://snipurl.com/v9v3 Course web site: http://www.kddresearch.org/Courses/CIS730http://www.kddresearch.org/Courses/CIS730 Instructor home page: http://www.cis.ksu.edu/~bhsuhttp://www.cis.ksu.edu/~bhsu Reading for Next Class: Section 8.3 – 8.4, p. 253 - 266, Russell & Norvig 2 nd edition Handout, Nilsson & Genesereth, Logical Foundations of Artificial Intelligence Intro to First-Order Logic: Syntax and Semantics
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Lecture Outline Reading for Next Class: 8.3-8.4 (p. 253-266), 9.1 (p. 272-274), R&N 2 e Last Class: Propositional Logic, Sections 7.5-7.7 (p. 211-232), R&N 2 e Properties of sentences (and sets of sentences, aka knowledge bases) entailment provability/derivability validity: truth in all models (aka tautological truth) satisfiability: truth in some models 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) 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 2 e 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)
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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 Concluded
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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. Inference: Review
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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. Validity and Satisfiability: Review
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Forward Chaining Example: Review Adapted from slides © 2004 S. Russell & P. Norvig. Reused with permission. 2 2 2 21 n: number of antecedents (LHS conjuncts) still unmatched 1 1 2 21 1 0 1 21 1 0 0 11 1 0 0 0 1 0 0 0 00 0 0 0 00
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Backward Chaining Example: Review © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Forward vs. Backward Chaining: Review © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Resolution [1]: Propositional Sequent Rule Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Resolution [2]: Conversion to Conjunctive Normal Form (CNF) Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Resolution [3]: Algorithm Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Resolution [4]: Example Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Chapter 7: Summary © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Chapter 8: Overview © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Propositional Logic: Pros and Cons Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence First-Order Logic (FOL) Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial 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
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Syntax of FOL: Basic Elements © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial 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)”
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Complex Sentences © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Truth in First-Order Logic © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Models for FOL: Example © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Models for FOL: Example © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Models for FOL: Lots! © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Universal Quantification [1]: Definition Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Universal Quantification [2]: Common Mistake to Avoid Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Existential Quantification [1]: Definition Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Existential Quantification [2]: Common Mistake to Avoid Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Properties of Quantifiers © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Fun With Sentences Adapted from slides © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Equality © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Interacting with FOL KBs © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Knowledge Base for Wumpus World Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Deducing Hidden Properties © 2004 S. Russell & P. Norvig. Reused with permission.
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial Intelligence Terminology First-Order Logic (FOL) aka First-Order Predicate Calculus (FOPC) Components Semantics (meaning, denotation): objects, functions, relations Syntax: constants, variables, terms, predicates Properties of sentences (and sets of sentences, aka knowledge bases) entailment provability/derivability validity: truth in all models (aka tautological truth) satisfiability: truth in some models 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) Conjunctive Normal Form (CNF) Universal Quantification (“For All”) Existential Quantification (“Exists”)
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Computing & Information Sciences Kansas State University Lecture 12 of 42 CIS 530 / 730 Artificial 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 semantics Relationship to Boolean algebra Properties 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
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