First-order modal logic

First-order modal logic / Melvin Fitting, Richard L. Mendelsohn.

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...

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Bibliographic Details
Main Authors: Fitting, Melvin, 1942- (Author), Mendelsohn, Richard L. (Author)
Format: eBook
Language:English
Published: Cham : Springer, [2023]
Edition:Second edition.
Series:Synthese library ; v. 480.
Subjects:
Modality (Logic)
Online Access:Click for online access
Table of Contents:
  • 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
  • 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
  • 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
  • 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
  • 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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