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Three Views of Logic Mathematics, Philosophy, and Computer Science [electronic resource]
Loveland, Donald W
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| 자료유형 | E-BOOK |
|---|---|
| 서명/저자사항 | Three Views of Logic [electronic resource]: Mathematics, Philosophy, and Computer Science/ Donald W. Loveland. |
| 개인저자 | Loveland, Donald W, Hodel, Richard E, Sterrett, S. G, |
| 발행사항 | Princeton: Princeton University Press, 2014. |
| 형태사항 | 1 online resource (339 pages). |
| 기타형태 저록 | Print version: Loveland, Donald W. Three Views of Logic : Mathematics, Philosophy, and Computer Science. Princeton : Princeton University Press, 2014 9780691160443 |
| ISBN | 9781400848751 140084875X 9780691160443 0691160449 |
| 일반주기 |
9.9 Intuitive Descriptions of the Four-Valued Logic Semantics.
|
| 서지주기 | Includes bibliographical references at the end of each chapters and index. |
| 내용주기 | Cover; Title; Copyright; Contents; Preface; Acknowledgments; PART 1. Proof Theory; 1 Propositional Logic; 1.1 Propositional Logic Semantics; 1.2 Syntax: Deductive Logics; 1.3 The Resolution Formal Logic; 1.4 Handling Arbitrary Propositional Wffs; 2 Predicate Logic; 2.1 First-Order Semantics; 2.2 Resolution for the Predicate Calculus; 2.2.1 Substitution; 2.2.2 The Formal System for Predicate Logic; 2.2.3 Handling Arbitrary Predicate Wffs; 3 An Application: Linear Resolution and Prolog; 3.1 OSL-Resolution; 3.2 Horn Logic; 3.3 Input Resolution and Prolog; Appendix A: The Induction Principle. Appendix B: First-Order ValuationAppendix C: A Commentary on Prolog; References; PART 2. Computability Theory; 4 Overview of Computability; 4.1 Decision Problems and Algorithms; 4.2 Three Informal Concepts; 5 A Machine Model of Computability; 5.1 Register Machines and RM-Computable Functions; 5.2 Operations with RM-Computable Functions; Church-Turing Thesis; LRM-Computable Functions; 5.3 RM-Decidable and RM-Semi-Decidable Relations; the Halting Problem; 5.4 Unsolvability of Hilbert's Decision Problem and Thue's Word Problem; 6 A Mathematical Model of Computability. 6.1 Recursive Functions and the Church-Turing Thesis6.2 Recursive Relations and RE Relations; 6.3 Primitive Recursive Functions and Relations; Coding; 6.4 Kleene Computation Relation Tn(e, a1 ..., an, c); 6.5 Partial Recursive Functions; Enumeration Theorems; 6.6 Computability and the Incompleteness Theorem; List of Symbols; References; PART 3. Philosophical Logic; 7 Non-Classical Logics; 7.1 Alternatives to Classical Logic vs. Extensions of Classical Logic; 7.2 From Classical Logic to Relevance Logic; 7.2.1 The (So-Called) "Paradoxes of Implication." 7.2.2 Material Implication and Truth Functional Connectives7.2.3 Implication and Relevance; 7.2.4 Revisiting Classical Propositional Calculus: What to Save, What to Change, What to Add?; 8 Natural Deduction: Classical and Non-Classical; 8.1 Fitch's Natural Deduction System for Classical Propositional Logic; 8.2 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Necessity; 8.3 Revisiting Fitch's Rules of Natural Deduction to Better Formalize the Notion of Entailment-Relevance; 8.4 The Rules of System FE (Fitch-Style Formulation of the Logic of Entailment). 8.5 The Connective "Or," Material Implication, and the Disjunctive Syllogism9 Semantics for Relevance Logic: A Useful Four-Valued Logic; 9.1 Interpretations, Valuations, and Many Valued Logics; 9.2 Contexts in Which This Four-Valued Logic Is Useful; 9.3 The Artificial Reasoner's (Computer's) "State of Knowledge"; 9.4 Negation in This Four-Valued Logic; 9.5 Lattices: A Brief Tutorial; 9.6 Finite Approximation Lattices and Scott's Thesis; 9.7 Applying Scott's Thesis to Negation, Conjunction, and Disjunction; 9.8 The Logical Lattice L4. |
| 요약 | Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and fir. |
| 일반주제명 | Proof theory. Computable functions. Nonclassical mathematical logic. Computable functions. Logic, Symbolic and mathematical. Mathematics --Philosophy. Nonclassical mathematical logic. Proof theory. MATHEMATICS --General. MATHEMATICS --Linear & Nonlinear Programming. Computable functions. Nonclassical mathematical logic. Proof theory. |
| 언어 | 영어 |
| 바로가기 | URL |
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