Three Views of Logic:  Mathematics, Philosophy, and Computer Science
Publisher: Princeton University Press
Published: 2014
Format: Paperback; ebook (Kindle)
Number of pages: 322
ISBN-13: 9781400848751
Table of contents: title: TABLE OF CONTENTS:; title: Preface ix; title: Acknowledgments xiii; title: PART 1. Proof Theory 1; title: Donald Loveland; title: 1 Propositional Logic 3; title: 1.1 Propositional Logic Semantics 5; title: 1.2 Syntax: Deductive Logics 13; title: 1.3 The Resolution Formal Logic 14; title: 1.4 Handling Arbitrary Propositional Wffs 26; title: 2 Predicate Logic 31; title: 2.1 First-Order Semantics 32; title: 2.2 Resolution for the Predicate Calculus 40; title: 2.2.1 Substitution 41; title: 2.2.2 The Formal System for Predicate Logic 45; title: 2.2.3 Handling Arbitrary Predicate Wffs 54; title: 3 An Application: Linear Resolution and Prolog 61; title: 3.1 OSL-Resolution 62; title: 3.2 Horn Logic 69; title: 3.3 Input Resolution and Prolog 77; title: Appendix A: The Induction Principle 81; title: Appendix B: First-Order Valuation 82; title: Appendix C: A Commentary on Prolog 84; title: References 91; title: PART 2. Computability Theory 93; title: Richard E. Hodel; title: 4 Overview of Computability 95; title: 4.1 Decision Problems and Algorithms 95; title: 4.2 Three Informal Concepts 107; title: 5 A Machine Model of Computability 123; title: 5.1 RegisterMachines and RM-Computable Functions 123; title: 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions 136; title: 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem 144; title: 5.4 Unsolvability of Hilbert's Decision Problem and Thue'sWord Problem 154; title: 6 A Mathematical Model of Computability 165; title: 6.1 Recursive Functions and the Church-Turing Thesis 165; title: 6.2 Recursive Relations and RE Relations 175; title: 6.3 Primitive Recursive Functions and Relations; Coding 187; title: 6.4 Kleene Computation Relation Tn(e, a1, . . . , an, c) 197; title: 6.5 Partial Recursive Functions; Enumeration Theorems 203; title: 6.6 Computability and the Incompleteness Theorem 216; title: List of Symbols 219; title: References 220; title: PART 3. Philosophical Logic 221; title: S. G. Sterrett; title: 7 Non-Classical Logics 223; title: 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic 223; title: 7.2 From Classical Logic to Relevance Logic 228; title: 7.2.1 The (So-Called) "Paradoxes of Implication" 228; title: 7.2.2 Material Implication and Truth Functional Connectives 234; title: 7.2.3 Implication and Relevance 238; title: 7.2.4 Revisiting Classical Propositional Calculus: What to Save,What to Change, What to Add? 240; title: 8 Natural Deduction: Classical and Non-Classical 243; title: 8.1 Fitch's Natural Deduction System for Classical Propositional Logic 243; title: 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity 251; title: 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance 253; title: 8.4 The Rules of System FE (Fitch-Style Formulation ofthe Logic of Entailment) 261; title: 8.5 The Connective "Or," Material Implication,and the Disjunctive Syllogism 281; title: 9 Semantics for Relevance Logic: A Useful Four-Valued Logic 288; title: 9.1 Interpretations, Valuations, and Many Valued Logics 288; title: 9.2 Contexts in Which This Four-Valued Logic Is Useful 290; title: 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge" 291; title: 9.4 Negation in This Four-Valued Logic 295; title: 9.5 Lattices: A Brief Tutorial 297; title: 9.6 Finite Approximation Lattices and Scott's Thesis 302; title: 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction 304; title: 9.8 The Logical Lattice L4 307; title: 9.9 Intuitive Descriptions of the Four-Valued Logic Semantics 309; title: 9.10 Inferences and Valid Entailments 312; title: 10 Some Concluding Remarks on the Logic of Entailment 315; title: References 316; title: Index 319