First-Order Modal Logic

First-Order Modal Logic by M. Fitting, Richard L. Mendelsohn.

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 provid...

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Bibliographic Details
Main Authors: Fitting, M. (Author), Mendelsohn, Richard L. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1998.
Edition:1st ed. 1998.
Series:Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; 277
Springer eBook Collection.
Subjects:
Logic.
Mathematical logic.
Computational linguistics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • One/Propositional Modal Logic
  • 1.1 What is a Modal?
  • 1.2 Can There Be a Modal Logic?
  • 1.3 What Are The Formulas?
  • 1.4 Aristotle’s Modal Square
  • 1.5 Informal Interpretations
  • 1.6 What Are the Models?
  • 1.7 Examples
  • 1.8 Some Important Logics
  • 1.9 Logical Consequence
  • 1.10 Temporal Logic
  • 1.11 Epistemic Logic
  • 1.12 Historical Highlights
  • Two/Tableau Proof Systems
  • 2.1 What Is a Proof
  • 2.2 Tableaus
  • 2.3 More Tableau Systems
  • 2.4 Logical Consequence and Tableaus
  • 2.5 Tableaus Work
  • Three/Axiom Systems
  • 3.1 What Is an Axiomatic Proof
  • 3.2 More Axiom Systems
  • 3.3 Logical Consequence, Axiomatically
  • 3.4 Axiom Systems Work Too
  • Four/Quantified Modal Logic
  • 4.1 First-Order Formulas
  • 4.2 An Informal Introduction
  • 4.3 Necessity De Re and De Dicto
  • 4.4 Is Quantified Modal Logic Possible?
  • 4.5 What the Quantifiers Quantify Over
  • 4.6 Constant Domain Models
  • 4.7 Varying Domain Models
  • 4.8 Different Media, Same Message
  • 4.9 Barcan and Converse Barcan Formulas
  • Five/First-Order Tableaus
  • 5.1 Constant Domain Tableaus
  • 5.2 Varying Domain Tableaus
  • 5.3 Tableaus Still Work
  • Six/First-Order Axiom Systems
  • 6.1 A Classical First-Order Axiom System
  • 6.2 Varying Domain Modal Axiom Systems
  • 6.3 Constant Domain Systems
  • 6.4 Miscellany
  • Seven/Equality
  • 7.1 Classical Background
  • 7.2 Frege’s Puzzle
  • 7.3 The Indiscernibility of Identicals
  • 7.4 The Formal Details
  • 7.5 Tableau Equality Rules
  • 7.6 Tableau Soundness and Completeness
  • 7.7 An Example
  • Eight/Existence and Actualist Quantification
  • 8.1 To Be
  • 8.2 Tableau Proofs
  • 8.3 The Paradox of NonBeing
  • 8.4 Deflationists
  • 8.5 Parmenides’ Principle
  • 8.6 Inflationists
  • 8.7 Unactualized Possibles
  • 8.8 Barcan and Converse Barcan, Again
  • 8.9 Using Validities in Tableaus
  • 8.10 On Symmetry
  • Nine/Terms and Predicate Abstraction
  • 9.1 Why constants should not be constant
  • 9.2 Scope
  • 9.3 Predicate Abstraction
  • 9.4 Abstraction in the Concrete
  • 9.5 Reading Predicate Abstracts
  • Ten/Abstraction Continued
  • 10.1 Equality
  • 10.2 Rigidity
  • 10.3 A Dynamic Logic Example
  • 10.4 Rigid Designators
  • 10.5 Existence
  • 10.6 Tableau Rules, Varying Domain
  • 10.7 Tableau Rules, Constant Domain
  • Eleven/Designation
  • 11.1 The Formal Machinery
  • 11.2 Designation and Existence
  • 11.3 Existence and Designation
  • 11.4 Fiction
  • 11.5 Tableau Rules
  • Twelve/Definite Descriptions
  • 12.1 Notation
  • 12.2 Two Theories of Descriptions
  • 12.3 The Semantics of Definite Descriptions
  • 12.4 Some Examples
  • 12.5 Hintikka’s Schema and Variations
  • 12.6 Varying Domain Tableaus
  • 12.7 Russell’s Approach
  • 12.8 Possibilist Quantifiers
  • References.

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