First-Order Modal Logic - Fitting, M.; Mendelsohn, Richard L.; SpringerLink (Online service) (Dordrecht : Springer Netherlands : Imprint: Springer, 1998)
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.
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$1 (Bs 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$1 (Bs 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$1 (BPrinciple -- 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$1 (Bs Schema and Variations -- 12.6 Varying Domain Tableaus -- 12.7 Russell$1 (Bs Approach -- 12.8 Possibilist Quantifiers -- References.s
Keywords: Logic; Mathematical logic; Computational linguistics; Logic; Mathematical Logic and Foundations; Computational Linguistics