Three Views of Logic: Mathematics, Philosophy, and Computer Science - Info and Reading Options

"Three Views of Logic: Mathematics, Philosophy, and Computer Science" Table Of Contents:

• 1- TABLE OF CONTENTS:
• 2- Preface ix
• 3- Acknowledgments xiii
• 4- PART 1. Proof Theory 1
• 5- Donald Loveland
• 6- 1 Propositional Logic 3
• 7- 1.1 Propositional Logic Semantics 5
• 8- 1.2 Syntax: Deductive Logics 13
• 9- 1.3 The Resolution Formal Logic 14
• 10- 1.4 Handling Arbitrary Propositional Wffs 26
• 11- 2 Predicate Logic 31
• 12- 2.1 First-Order Semantics 32
• 13- 2.2 Resolution for the Predicate Calculus 40
• 14- 2.2.1 Substitution 41
• 15- 2.2.2 The Formal System for Predicate Logic 45
• 16- 2.2.3 Handling Arbitrary Predicate Wffs 54
• 17- 3 An Application: Linear Resolution and Prolog 61
• 18- 3.1 OSL-Resolution 62
• 19- 3.2 Horn Logic 69
• 20- 3.3 Input Resolution and Prolog 77
• 21- Appendix A: The Induction Principle 81
• 22- Appendix B: First-Order Valuation 82
• 23- Appendix C: A Commentary on Prolog 84
• 24- References 91
• 25- PART 2. Computability Theory 93
• 26- Richard E. Hodel
• 27- 4 Overview of Computability 95
• 28- 4.1 Decision Problems and Algorithms 95
• 29- 4.2 Three Informal Concepts 107
• 30- 5 A Machine Model of Computability 123
• 31- 5.1 RegisterMachines and RM-Computable Functions 123
• 32- 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions 136
• 33- 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem 144
• 34- 5.4 Unsolvability of Hilbert's Decision Problem and Thue'sWord Problem 154
• 35- 6 A Mathematical Model of Computability 165
• 36- 6.1 Recursive Functions and the Church-Turing Thesis 165
• 37- 6.2 Recursive Relations and RE Relations 175
• 38- 6.3 Primitive Recursive Functions and Relations; Coding 187
• 39- 6.4 Kleene Computation Relation Tn(e, a1, . . . , an, c) 197
• 40- 6.5 Partial Recursive Functions; Enumeration Theorems 203
• 41- 6.6 Computability and the Incompleteness Theorem 216
• 42- List of Symbols 219
• 43- References 220
• 44- PART 3. Philosophical Logic 221
• 45- S. G. Sterrett
• 46- 7 Non-Classical Logics 223
• 47- 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic 223
• 48- 7.2 From Classical Logic to Relevance Logic 228
• 49- 7.2.1 The (So-Called) "Paradoxes of Implication" 228
• 50- 7.2.2 Material Implication and Truth Functional Connectives 234
• 51- 7.2.3 Implication and Relevance 238
• 52- 7.2.4 Revisiting Classical Propositional Calculus: What to Save,What to Change, What to Add? 240
• 53- 8 Natural Deduction: Classical and Non-Classical 243
• 54- 8.1 Fitch's Natural Deduction System for Classical Propositional Logic 243
• 55- 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity 251
• 56- 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance 253
• 57- 8.4 The Rules of System FE (Fitch-Style Formulation ofthe Logic of Entailment) 261
• 58- 8.5 The Connective "Or," Material Implication,and the Disjunctive Syllogism 281
• 59- 9 Semantics for Relevance Logic: A Useful Four-Valued Logic 288
• 60- 9.1 Interpretations, Valuations, and Many Valued Logics 288
• 61- 9.2 Contexts in Which This Four-Valued Logic Is Useful 290
• 62- 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge" 291
• 63- 9.4 Negation in This Four-Valued Logic 295
• 64- 9.5 Lattices: A Brief Tutorial 297
• 65- 9.6 Finite Approximation Lattices and Scott's Thesis 302
• 66- 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction 304
• 67- 9.8 The Logical Lattice L4 307
• 68- 9.9 Intuitive Descriptions of the Four-Valued Logic Semantics 309
• 69- 9.10 Inferences and Valid Entailments 312
• 70- 10 Some Concluding Remarks on the Logic of Entailment 315
• 71- References 316
• 72- Index 319

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