Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Lecture 13 of 42 William H. Hsu Department of Computing and Information Sciences, KSU KSOL course page: Course web site: Instructor home page: Reading for Next Class: Section 9.2 – 9.4, p , Russell & Norvig 2 nd edition Handout, Nilsson & Genesereth, Logical Foundations of Artificial Intelligence FOL: The Frame Problem, Situation Calculus, and First-Order Inference

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Lecture Outline Reading for Next Class: Sections 9.2 – 9.4 (p. 275 – 294), R&N 2 e Last Class: Intro to FOL, Sections (p ), R&N 2 e  Elements of logic: ontology and epistemology  First-order predicate calculus (FOPC) aka first order logic (FOL)  Properties of sentences (and sets of sentences, aka knowledge bases)  entailment vs. provability/derivability  validity vs. satisfiability  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) Today: KR in FOL, Sections (p ), 9.1 (p ), R&N 2 e  Frame problem: representational (frame axioms) vs. inferential  Related inference problems: ramification and qualification  Situation calculus  First-order inference: Generalized Modus Ponens (GMP) This Week: KR and Inference in First-Order Logic (Ch. 8 – 10)

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence © 2004 S. Russell & P. Norvig. Reused with permission. Soundness and Completeness in FOL: Review

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Resolution – Algorithm: Review Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Resolution – Example: Review Adapted from slide © 2004 S. Russell & P. Norvig. Reused with permission. Antecedents (Precedents) Resolvent (Consequent)

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Ontology and Epistemology: Review 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 Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Denotational Semantics of FOL: Review Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Automated Deduction: Review © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Keeping Track of Change © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Describing Actions [1]: Frame Axioms and the Frame Problem Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Describing Actions [2]: Successor-State Axioms Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Making Plans [1]: Naïve Approach – Theorem Proving Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Making Plans [2]: A Better Way – Planning Systems Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Chapter 8: Summary © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Chapter 9: Outline © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence A Brief History of Reasoning © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Universal Instantiation (UI) © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Existential Instantiation (EI) © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Using Universal and Existential Instantiation Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Reduction to Propositional Inference [1]: Ground Terms Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Reduction to Propositional Inference [2]: Herbrand’s Lifting Lemma Based on slide © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Problems with Propositionalization © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Unification: Preview Adapted from slides © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Generalized Modus Ponens (GMP) © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Soundness of GMP © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Example Knowledge Base: Preview © 2004 S. Russell & P. Norvig. Reused with permission.

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Terminology Resolution: Sound and Complete Inference Rule/Procedure for FOL  Antecedent (aka precedent): sentences “above line” in sequent rule  Resolvent (aka consequent): sentences “below line” in sequent rule Forward Chaining: Systematic Application of Rule to Whole KB  Rete algorithm in production systems for expert systems development  Susceptible to high fan-out (branch factor) Backward Chaining: Goal-Directed Today: Representing States/Actions in FOL; Propositional Logic to FOL  Frame problem  representational: proliferation of frame axioms  inferential: replication of state  Qualification problem: handling “exceptions” (contingencies)  Ramification problem: handling “side effects”  Situation calculus: FOL-based language; successor state axioms, situations  Herbrand’s lifting lemma: can generalize from propositional inference  Propositionalization: mapping down to ground terms

Computing & Information Sciences Kansas State University Lecture 13 of 42 CIS 530 / 730 Artificial Intelligence Last Class: Overview of Knowledge Representation (KR) and FOL  Syntax and semantics  Ontological vs. epistemological commitments  Sentences: entailment vs. provability/derivability, validity vs. satisfiability  Proof rules  soundness: KB ⊢ i α  KB ⊨ α (can prove only true sentences)  completeness: KB ⊨ α  KB ⊢ i α (can prove all true sentences) Today: Representing States and Actions in FOL  Frame problem  representational: proliferation of frame axioms  inferential: replication of state  Relatives: ramification problem and qualification problem  Partial solution to representational frame problem: situation calculus Chapter 9: First-Order Inference  Herbrand theory: ground terms, lifting lemma  Preview of unification, GMP Summary Points