Epistemic Situation Calculus Based on Granular Computing: A New Approach to Common-Sense Reasoning (Intelligent Systems Reference Library, 239)

Description

This book approaches to the subject of common-sense reasoning in AI using epistemic situation calculus which integrates the ideas of situation calculus and epistemic logic. Artificial intelligence (AI) is the research area of science and engineering for intelligent machines, especially intelligent computer programs. It is very important to deal with common-sense reasoning in knowledge-based systems. If we employ a logic-based framework, classical logic is not suited for the purpose of describing common-sense reasoning. It is well known that there are several difficulties with logic-based approaches, e.g., the so-called Fame Problem. We try to formalize common-sense reasoning in the context of granular computing based on rough set theory. The book is intended for those, like experts and students, who wish to get involved in the field as a monograph or a textbook for the subject. We assume that the reader has mastered the material ordinarily covered in AI and mathematical logic Foreword Preface Contents 1 Introduction 1.1 Motivations 1.2 Organization References 2 Preliminaries 2.1 Rough Set Theory 2.1.1 Pawlak's Rough Set Theory 2.1.2 Variable Precision Rough Set 2.1.3 Decision Logic 2.2 Decision Tables 2.2.1 Definitions 2.2.2 Simplification 2.3 Non-Classical Logics 2.3.1 Modal Logic 2.3.2 Many-Valued Logic 2.3.3 Bilattice Logics 2.3.4 Relevance Logic 2.4 Basic Situation Calculus 2.4.1 Foundational Axioms for Situations 2.4.2 Domain Axioms and Basic Theories of Actions 2.4.3 The Frame Problem 2.4.4 Frame Axioms References 3 Deduction Systems Based on Rough Sets 3.1 Introduction 3.2 Rough Sets and Decision Logic 3.2.1 Decision Tables 3.2.2 Decision Logic 3.3 Belnap's Four-Valued Logic 3.4 Rough Sets and Partial Semantics 3.5 Consequence Relation and Sequent Calculus 3.6 Extension of Many-Valued Semantics 3.7 Soundness and Completeness 3.8 Conclusion and Future Work References 4 Tableaux Calculi for Many-Valued Logics 4.1 Introduction 4.2 Backgrounds 4.2.1 Rough Set and Decision Logic 4.2.2 Variable Precision Rough Set 4.2.3 Belnap's Four-Valued Logic 4.2.4 Analytic Tableaux 4.3 Tableaux Calculi for Many-Valued Logics 4.3.1 Relationship with Four-Valued Semantics 4.3.2 Many-Valued Tableaux Calculi 4.4 Soundness and Completeness 4.5 Concluding Remarks References 5 Granular Reasoning for the Epistemic Situation Calculus 5.1 Introduction 5.2 Epistemic Situation Calculus 5.2.1 Background of Lakemeyer & Levesque's Logic ES 5.2.2 Semantics of ES 5.2.3 Basic Action Theory 5.3 Rough Set and Decision Logic 5.3.1 Rough Set 5.3.2 Decision Logic 5.3.3 Variable Precision Rough Set 5.4 Zooming Reasoning 5.4.1 Kripke Model 5.4.2 Granularized Possible World and Zooming Reasoning 5.5 Consequence Relation for Partial Semantics 5.5.1 Belnap's Four-Valued Logic 5.5.2 Four-Valued Modal Logic 5.5.3 Semantic Relation with Four-Valued Logic 5.5.4 Consequence Relation and Sequent Calculus 5.6 Zooming Reasoning as Action 5.6.1 Zooming Reasoning in ES 5.6.2 Action Theory for Zooming Reasoning 5.6.3 Semantics for Zooming Reasoning in ES 5.7 Conclusion References 6 Discussion 6.1 The Frame Problem 6.1.1 What is the Frame Problem? 6.1.2 The Frame Problem in Logic 6.1.3 The Epistemological Frame Problem 6.2 Re-Examination of the Frame Problem in the Context of Granular Reasoning 6.2.1 Solution to the Frame Problem with the Situation Calculus 6.2.2 Dennett's Robot Scenario 6.3 Conclusion References 7 Conclusions 7.1 Summary and Achievements 7.2 Future Direction References Appendix Index Index