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▼a 9781400848751
▼q (electronic bk.) |
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▼a 140084875X
▼q (electronic bk.) |
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▼z 9781306282598 |
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▼z 1306282594 |
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▼a 9780691160443 |
| 020 | |
▼a 0691160449 |
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▼a (OCoLC)867317379 |
| 037 | |
▼a 22573/ctt4kd6d6
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▼a MAT018000
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▼a 511.3 |
| 100 | 1 |
▼a Loveland, Donald W. |
| 245 | 10 |
▼a Three Views of Logic
▼h [electronic resource] :
▼b Mathematics, Philosophy, and Computer Science. |
| 260 | |
▼a Princeton :
▼b Princeton University Press,
▼c 2014. |
| 300 | |
▼a 1 online resource (339 pages) |
| 336 | |
▼a text
▼b txt
▼2 rdacontent |
| 337 | |
▼a computer
▼b c
▼2 rdamedia |
| 338 | |
▼a online resource
▼b cr
▼2 rdacarrier |
| 500 | |
▼a 9.9 Intuitive Descriptions of the Four-Valued Logic Semantics. |
| 504 | |
▼a Includes bibliographical references at the end of each chapters and index. |
| 505 | 0 |
▼a 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. |
| 505 | 8 |
▼a 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. |
| 505 | 8 |
▼a 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." |
| 505 | 8 |
▼a 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). |
| 505 | 8 |
▼a 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. |
| 520 | |
▼a 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. |
| 588 | 0 |
▼a Print version record. |
| 650 | 0 |
▼a Proof theory. |
| 650 | 0 |
▼a Computable functions. |
| 650 | 0 |
▼a Nonclassical mathematical logic. |
| 650 | 4 |
▼a Computable functions. |
| 650 | 4 |
▼a Logic, Symbolic and mathematical. |
| 650 | 4 |
▼a Mathematics
▼x Philosophy. |
| 650 | 4 |
▼a Nonclassical mathematical logic. |
| 650 | 4 |
▼a Proof theory. |
| 650 | 7 |
▼a MATHEMATICS
▼x General.
▼2 bisacsh |
| 650 | 7 |
▼a MATHEMATICS
▼x Linear & Nonlinear Programming.
▼2 bisacsh |
| 650 | 7 |
▼a Computable functions.
▼2 fast
▼0 (OCoLC)fst00871985 |
| 650 | 7 |
▼a Nonclassical mathematical logic.
▼2 fast
▼0 (OCoLC)fst01038606 |
| 650 | 7 |
▼a Proof theory.
▼2 fast
▼0 (OCoLC)fst01078942 |
| 655 | 4 |
▼a Electronic books. |
| 655 | 0 |
▼a Electronic books. |
| 700 | 1 |
▼a Hodel, Richard E. |
| 700 | 1 |
▼a Sterrett, S. G. |
| 776 | 08 |
▼i Print version:
▼a Loveland, Donald W.
▼t Three Views of Logic : Mathematics, Philosophy, and Computer Science.
▼d Princeton : Princeton University Press, 짤2014
▼z 9780691160443 |
| 856 | 40 |
▼3 EBSCOhost
▼u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=639113 |
| 938 | |
▼a EBL - Ebook Library
▼b EBLB
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▼a EBSCOhost
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| 938 | |
▼a Ingram Digital eBook Collection
▼b IDEB
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| 938 | |
▼a YBP Library Services
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▼a 관리자 |