First-Order Modal Logic

Description

New York: Springer. 1998/ 300 p. ISBN 978-0-7923-5335-5; ISBN 978-94-011-5292-1 (eBook)This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.Table of contentsPrefacePropositional Modal LogicWhat is a Modal?Can There Be a Modal Logic?What Are The Formulas?Aristotle's Modal SquareInformal Inlcrprc tat ionsWhat Are the Models?ExamplesSome Important logicsLogical ConsequenceTemporal LogicEpistcmic LogicHistorical HighlightsTableau Proof SystemsWhat Is a ProofTableausMore Tableau SystemsLogical Consequence and Tableau*Tableaus WorkAxiom SystemsWhat Is an Axiomatic ProofMore Axiom SystemsLogical Consequence. AxiomaticallyAxiom Systems Work TooQuantified Modal LogicFirst-Order FormulasAn Informal IntroductionNecessity De Re and Dc DictoIs Quantified Modal l-ogic Possible?What the Quantifiers Quantify OverConstant Domain ModelsVarying Domain ModelsDifferent Media, Same MessageBarcan and Converse Bare an FormulasFirst-order tableausConstant Domain TableausVarying Domain TableausTableaus Still WorkFirst-Order Axiom SystemsA Classical First-Order Axiom SystemVarying Domain Modal Axiom SystemsConstant Domain SystemsMiscellanyEqualityClassical BackgroundFrege's PuzzleThe Indiscernibility of IdenticalsThe Formal DetailsTableau Equality RulesTableau Soundness and CompletenessAn ExampleExistence and actualist quantificationTo BeTableau ProofsThe Paradox of NonBcingDeflationistsParmenides' PrincipleInflationistsUnactualized PossiblesBarcan and Converse Barcan, AgainUsing Validities in TableausOn SymmetryTerms and Predicate AbstractionWhy constants should not be constantScopePredicate AbstractionAbstraction in the ConcreteReading Predicate AbstractsAbstraction continuedEqualityRigidityA Dynamic Logic ExampleRigid DesignatorsExistenceTableau Rules, Varying DomainTableau Rules, Constant DomainDesignationThe Formal MachineryDesignation and ExistenceExistence and DesignationFictionTableau RulesDefinite DescriptionsNotationTwo Theories of DescriptionsThe Semantics of Definite DescriptionsSome ExamplesHintikka's Schema and VariationsVarying Domain TableausRussell's ApproachPossibilist QuantifiersReferencesIndex