Logic works : a rigorous introduction to formal logic /: a rigorous introduction to formal logic. (2021)

• Record Type: Book
• Further Information: Note: Lorne Falkenstein, Scott Stapleford and Molly Kao.
• Authors: Falkenstein, Lorne; Stapleford, Scott; Kao, Molly, 1986-
• Contents: Preface; Symbol Summary 1. Introduction to the study of logic; 1.1 Demonstration and interpretation 1.2 Deductive and inductive demonstrations 1.3 The principle of noncontradiction 1.4 Abstraction, variables, and formalization; logical and nonlogical elements; formal contradiction 1.5 A fundamental problem 1.6 Outline of forthcoming chapters Appendix: Elements of a theory of demonstrative logic Part I: Sentential Logic 2. Vocabulary and syntax; 2.1: Introduction Syntax 2.2: Conventions 2.3: Syntactic demonstrations and trees 2.4: Scope; named forms 2.5: Formal properties 3. Semantics; 3.1: Semantics for ⊥ and the sentence letters 3.2: Semantics for the connectives 3.3: Semantics for compound sentences 3.4: Intensional concepts Appendix: Expressive adequacy; disjunctive normal form; the lean language 4. Formalization; 4.1: Looseness of fit 4.2: Conditional sentences of English 4.3: Necessary conditions 4.4: Sufficient conditions 4.5: Necessary and sufficient conditions; the principle of charity 4.6: Formalizing necessary and sufficient conditions 4.7: Exceptions and strong exceptions 4.8: Disjunction 4.9: Negations and conjunctions 4.10: Punctuation 4.11: Limits of formalization 4.12: Formalizing demonstrations 5. Working with SL semantics; 5.1: Identifying and verifying interpretations 5.2: Demonstrating that there is no interpretation 5.3: Demonstrating general principles 5.4: Falsifying general claims 5.5: Relations between intensional concepts; models; entailment Appendix: Alternatives to bivalence A-1. Advanced topics concerning SL semantics; A-1.1: Mathematical induction A-1.2: Bivalence A-1.3: Extensionality A-1.4: Compactness 6. Derivations; 6.1: DL : a lean derivation system 6.2: Strategies for doing derivations in DL 6.3: Ds: a derivation system for SL 6.4: Strategies for doing derivations in Ds 6.5: Extensions of Ds; bracket free notation 6.6: Intuition and "Intuitionism"; derivation in intuitionistic logic A-2. Advanced topics concerning the soundness and completeness of Ds; A-2.1: Soundness A-2.2: Corollary results; consistency and extensionality A-2.3: Henkin completeness A-2.4: Proof of the Lindenbaum lemma A-2.5: Proof of lemma 2 A-2.6: Proof of lemma 3 A-2.7: Corollary results A-2.8: Post / Hilbert-Ackermann completeness 7. Reduction Trees; 7.1: Method and strategies 7.2: Using trees to determine derivability 7.3: Theory and definitions Appendix: Trees for three valued and paraconsistent logic A-3: Advanced topics concerning the soundness and completeness of Ts ; A-3.1: Soundness of Ts A-3.2: Completeness of Ts A-3.3: Decidability of Ts A-3.4: Converting trees to derivations; using Ts to prove the completeness of Ds Part II: Modal sentential logic 8. Vocabulary, syntax, formalization and derivations; 8.1: Vocabulary and syntax 8.2: Formalization 8.3: Derivations 9. Semantics and Trees for Modal and Intuitionistic Sentential Logic; 9.1: Semantics for MSL 9.2: Reduction trees for MSL 9.3: Semantics for ISL 9.4: Reduction trees for ISL A-4: Advanced Topics concerning the "soundness" and "completeness" of Dm and Tm; A-4.1: "Soundness" of the modal derivation systems A-4.2: Completeness of Tm A-4.3: Tree conversions A-4.4: Adequacy of Dm and Tm Part III: Predicate sentential logic 10. Vocabulary, syntax, formalization, and derivations; 10.1: English predication 10.2: Simple terms 10.3: Complex terms 11. Semantics and trees; 11.1: Interpretations 11.2: Valuation rules 11.3: Working with the semantics 11.4: Tp 11.5: Semantics for functional terms 11.6: Tpf 11.7: Semantics for definite descriptions A-5: Advanced topics for PSL; A-5.1: Extensionality and variance A-5.2: Soundness of Dp A-5.3: Completeness of Tp A-5.4: Tree conversion; soundness of Tp; completeness of Dp Part IV: Quantified Predicate Logic 12. Vocabulary, syntax, and formalization; 12.1: Informal vocabulary and syntax 12.2: Formal vocabulary and syntax 12.3: Formalizing English sentences in QPL 13. Derivations; 13.1: Dq 13.2: Extensions of Dq 14. Trees and tree model semantics for QPL; 14.1: Rules 14.2: Method 14.3: Tree model semantics 14.4: Extensions of Tq 15. Semantics for QPL without mixed multiple quantification; 15.1: Objectual semantics 15.2: Denotation 15.3: Satisfaction 15.4: Truth 15.5: Working with the semantics 15.6: Demonstrating general principles 16. Semantics for QPL with mixed multiple quantification; 16.1: Variants on variable assignments; denotation of variables 16.2: Satisfaction conditions for quantified formulas 16.3: (P) and (=) applications 16.4: Truth 16.5: Working with the semantics Appendix: Demonstration of the exclusivity principle A-6: Advanced topics for QPL; A-6.1: Extensionality and variance A-6.2:</ST
• Edition: 1st
• Publisher Details: London : Routledge
• Publication Date: 2021
• Extent: 1 online resource
• Subjects: 160; Logic
• Languages: English
• ISBNs: 9781000451306; 9781000451276; 9781003026532
• Related ISBNs: 9780367460303; 9780367460297
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.