First-order modal logic
type: Item
instance of: scholarly article
title: First-order modal logic
zbMATH Open document ID: 1025.03001
author: Melvin Fitting
author: Richard L. Mendelsohn
published in: Synthese Library
publication date: 2003-05-14T00:00:00Z
review text: This is an introductory textbook to logics for first-order-languages with modal operators, expounding (in addition to standard topics) important material not previously found in other textbooks of the same field. The book approaches semantics using possible world, or Kripke, models and for most of the book the proof-theoretic techniques are systems based on semantic tableau rules. The axiomatic approach to propositional and first-order modal logic is presented only in two of the twelve chapters of the book. Also, no completeness and soundness proofs are offered for the different axiomatic modal formal systems characterized; the reader is rather referred to published works where such proofs can be found. Completeness and soundness proofs are provided for the systems based on semantic tableau rules. In addition to the technical expositions, there are brief and clear discussions of philosophical issues that motivate the development of the modal logics characterized in the book. Also, the book considers what bearing technical developments would have on well-known philosophical problems. Philosophical topics taken into account include the distinction between \textit{de dicto} and \textit{de re} necessity, the possibility of quantified modal logic, the range of quantifiers within modal contexts (and so the problems of actualism and possibilism), the nature of identity, the indiscernibility of identicals, existence and non-being, proper names and definite descriptions. In detail: after characterizing the semantics for propositional modal languages and different semantic tableau systems corresponding to such a semantics, the book initially considers first-order modal languages without (individual) constants and function symbols. Two semantic systems are formulated for these languages: one in which the domain assigned to (first-order) quantifiers varies from possible world to possible world and another in which such a domain is constant. The former semantic system is associa…
Mathematics Subject Classification ID: 03-01
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 1910248
zbMATH Keywords: first-order logic
zbMATH Keywords: semantic tableau rules
zbMATH Keywords: possible worlds semantics
zbMATH Keywords: actualism
zbMATH Keywords: possibilism
zbMATH Keywords: modal logic
zbMATH Keywords: textbook
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1910248