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|a 1405364745
|a 1417666302
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|a 9783031407147
|q electronic book
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|a 3031407148
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|a 10.1007/978-3-031-40714-7
|2 doi
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|a (OCoLC)1405368135
|z (OCoLC)1405364745
|z (OCoLC)1417666302
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|a BC199.M6
|b F58 2023
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|a HCDD
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|a Fitting, Melvin,
|d 1942-
|e author.
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|a First-order modal logic /
|c Melvin Fitting, Richard L. Mendelsohn.
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|a Second edition.
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|a Cham :
|b Springer,
|c [2023]
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|a 1 online resource (xx, 460 pages) :
|b illustrations
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a Synthese Library
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|a Studies in epistemology, logic, methodology, and philosophy of science ;
|v volume 480
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|a Includes bibliographical references and index.
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|a Intro -- Preface -- What's in This Book -- How to Read This Book -- Differences from the First Edition -- Acknowledgments -- Contents -- Part I Background: Propositional Classical Logic -- 1 Background: Propositional Language -- 1.1 Introduction -- 1.2 The Propositional Language -- 1.3 Using Induction -- Exercises -- 2 Background: Propositional Axiomatics -- 2.1 Truth Tables -- Exercises -- 2.2 Axiom Systems -- 2.3 The Goal and General Outline -- Exercises -- 2.4 Consistency and Lindenbaum's Lemma -- Exercises -- 2.5 Implication and the Deduction Theorem -- Exercises
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|a 2.6 The Other Connectives -- 2.6.1 Conjunction -- 2.6.2 Disjunction -- 2.6.3 Negation -- 2.6.4 Implication -- Exercises -- 2.7 Summary of Our Classical Axiom System -- Exercises -- 2.8 Completeness At Last -- 2.9 Redefining Consistency -- 3 Background: Propositional Tableaus -- 3.1 Tableaus -- Exercises -- 3.2 Logical Consequence Using Tableaus -- Exercises -- 3.3 Tableau Soundness -- Exercises -- 3.4 Tableau Completeness -- 3.4.1 Hintikka Sets -- 3.4.2 Completeness, Constructively -- 3.4.3 Tableau Completeness, Non-constructively -- 3.4.4 Coda -- Exercises
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|a 3.5 Strong Completeness and Compactness -- Exercises -- References -- Part II Propositional Modal Logic -- 4 Modal Logic, an Introduction -- 4.1 What Is a Modal? -- Exercises -- 4.2 Can There Be a Modal Logic? -- 4.3 Aristotle's Modal Square -- 4.4 Informal Interpretations -- Exercises -- 4.5 Temporal Interpretations -- Exercises -- 4.6 Historical Highlights -- 4.6.1 Aristotle's Development of the Square -- Exercises -- 4.6.2 Aristotle's Future Sea Battle -- Exercises -- 4.6.3 The Master Argument of Diodorus Cronus -- 4.6.4 The Once and Future Conditional -- 4.6.5 The Reality of Necessity
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|a References -- 5 Propositional Modal Logic -- 5.1 What Are the Formulas? -- Exercises -- 5.2 What Are the Models? -- Exercises -- 5.3 Examples -- Exercises -- 5.4 Modal Logics, Semantically Defined -- Exercises -- 5.5 The Modal Cube -- Exercises -- 5.6 Semantic Consequence -- Exercises -- References -- 6 Propositional Modal Axiom Systems -- 6.1 The Logic K Axiomatically -- Exercises -- 6.2 More Axiom Systems -- Exercises -- 6.3 Logical Consequence, Axiomatically -- Exercises -- 6.4 Axiom Systems Work -- 6.4.1 Soundness -- 6.4.2 Completeness -- Exercises -- 6.5 Informal Notes
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|a 6.5.1 Gödel's Intuitionistic Logic Interpretation -- 6.5.2 Epistemic Logic -- 6.5.3 The Knowability Paradox -- 6.6 Justification Logic -- Exercises -- References -- 7 Propositional Modal Tableaus -- 7.1 Tableaus -- Exercises -- 7.2 More Tableau Systems -- Exercises -- 7.3 Logical Consequence and Tableaus -- Exercises -- 7.4 Modal Tableau Soundness -- Exercises -- 7.5 Modal Hintikka Sets -- 7.6 Propositional Modal Tableau Completeness -- 7.6.1 Modal Tableau Completeness, Constructively -- 7.6.2 Logical Consequence -- 7.6.3 Modal Completeness, Non-constructively -- Exercises
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|a This revised edition of the highly recommended book "First-Order Modal Logic", originally published in 1998, contains both new and modified chapters reflecting the latest scientific developments. Fitting and Mendelsohn present a thorough treatment of first-order modal logic, together with some propositional background. They adopt throughout a threefold approach. Semantically, they use possible world models; the formal proof machinery is tableaus; and full philosophical discussions are provided of the way that technical developments bear on well-known philosophical problems. The book covers quantification itself, including the difference between actualist and possibilist quantifiers; equality, leading to a treatment of Frege's morning star/evening star puzzle; the notion of existence and the logical problems surrounding it; non-rigid constants and function symbols; predicate abstraction, which abstracts a predicate from a formula, in effect providing a scoping function for constants and function symbols, leading to a clarification of ambiguous readings at the heart of several philosophical problems; the distinction between nonexistence and nondesignation; and definite descriptions, borrowing from both Fregean and Russellian paradigms. Review of the First Edition: "This Text is an excellent and most useful volume. It is pitched correctly: the exercises are just right... It sets a high standard for anything following. It is to be highly recommended." (Bulletin of Symbolic Logic, 8:3).
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|a Online resource; title from PDF title page (SpringerLink, viewed October 24, 2023).
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|a Modality (Logic)
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|a Modality (Logic)
|2 fast
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|a Mendelsohn, Richard L.,
|e author.
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|i Print version:
|a Fitting, Melvin
|t First-Order Modal Logic
|d Cham : Springer International Publishing AG,c2023
|z 9783031407130
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| 830 |
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|a Synthese library ;
|v v. 480.
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| 856 |
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://link.springer.com/10.1007/978-3-031-40714-7
|y Click for online access
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|a SPRING-ALL2023
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|a 92
|b HCD
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