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Three Views of Logic : Mathematics, Philosophy, and Computer Science.
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 accessib...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.