Handbook of philosophical logic. Volume II: Extensions of classical logic
type: Item
instance of: scholarly article
title: Handbook of philosophical logic. Volume II: Extensions of classical logic
zbMATH Open document ID: 0572.03003
published in: Synthese Library
publication date: 1984-01-01T00:00:00Z
review text: [For a review of Volume I (1983) see Zbl 0538.03001.] The second volume of this handbook leaves the field of classical logic and enters the very field of non-classical logics with background in philosophical topics. The leitmotif of this volume is the semantical idea of possible worlds: all its 12 chapters treat topics which are influenced by this idea. Or, to put it in other words, the whole volume is concerned with intensional logics. Point of departure is chapter 1 by \textit{R. A. Bull} and \textit{K. Segerberg} on ''Basic modal logic'' (pp. 1-88) in which the authors first present a historical survey and a catalogue of (propositional) modal logics in the style of \textit{K. Segerberg}'s book [An essay in classical modal logic (1971; Zbl 0311.02028)] and later turn to the main model theoretical constructions and results in the field with, of course, the Kripke frames at the very core. This semantic idea too is essential for chapter 2 by \textit{J. P. Burgess} on ''Basic tense logic'' (pp. 89-133), where the basic operators and systems of tense logic are introduced, and where the characterizability of the structure of time by tense logical formulas is discussed as well as the decidability of tense logics and nonclassical tense operators. An outlook on some more ''exotic'' time structures, unfortunately with only few references, closes the considerations. Chapter 3 by \textit{R. H. Thomason} immediately unites both themes, it is on ''Combinations of tense and modality'' (pp. 135-165). The topic is treated from a more philosophical perspective with lesser emphasis on pure technicalities: the essential difficulty is to understand the meaning of such combinations of tenses and modalities, e.g. of what is meant with ''historical necessity''. Some considerations on deontic resp. conditional logic combined with historical necessity close the chapter. This really philosophical intermezzo is followed by chapter 4 on ''Correspondence theory'' (pp. 167-247), written by \tex…
Mathematics Subject Classification ID: 03-02
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 68Q65
Mathematics Subject Classification ID: 03C80
zbMATH DE Number: 3912344
zbMATH Keywords: intensional connectives
zbMATH Keywords: modal correspondence theory
zbMATH Keywords: possible worlds
zbMATH Keywords: intensional logics
zbMATH Keywords: modal logic
zbMATH Keywords: Kripke frames
zbMATH Keywords: tense logic
zbMATH Keywords: quantification
zbMATH Keywords: semantics
zbMATH Keywords: conditional logic
zbMATH Keywords: counterfactuals
zbMATH Keywords: self- reference
zbMATH Keywords: provability logic
zbMATH Keywords: dynamic logic
zbMATH Keywords: deontic logic
zbMATH Keywords: logic of questions
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3912344