Handbook of philosophical logic. Vol. 5
type: Item
instance of: scholarly article
title: Handbook of philosophical logic. Vol. 5
zbMATH Open document ID: 1065.03001
published in: Handbook of Philosophical Logic
publication date: 2005-05-25T00:00:00Z
review text: This volume contains four of the chapters from Vol.~3 of the first edition: ``Intuitionistic logic'' by \textit{D. van Dalen} (pp. 1--114); ``Dialogues as a foundation for intuitionistic logic'' by \textit{W. Felscher} (pp. 115--145); ``Free logic'' by \textit{E. Bencivenga} (pp. 147--196); and ``Partial logic'' by \textit{S. Blamey} (pp. 261--353). The chapter on intuitionistic logic has an additional 3rd section, ``Proof terms and the Curry-Howard isomorphism''; in (the new) Section 4 the author added a few remarks and references concerning the model theory of intuitionistic logic in an intuitionistic setting; the section on the creating (instead of ``creative'' in the former version) subject is enriched by some remarks concerning the relationships between Kripke's schema KS and the continuum, and essentially sketches a proof that ``KS + indecomposabilty of \(\mathbb{R}\)'' implies that there are no discontinuous functions on \(\mathbb{R}\). The list of references is also slightly extended. In the chapter on dialogues there is essentially only an additional reference which reappears (slightly less correct) as a reference to a short ``editor's note'' which is added at the end. And also in the chapter on free logics only some few references are added. But there is an additional chapter, ``More free logic'' (pp. 197--259) by \textit{S. Lehmann}. It surveys more recent results not contained in the older chapter from the first edition; however, there is a considerable overlap in the topics that are mentioned in both chapters -- which is not really effective but allows one to read the new chapter essentially independently from the older one. The chapter on partial logic has been extensively updated and partly rewritten. The details are given in the author's introduction.
Mathematics Subject Classification ID: 03-00
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03F55
zbMATH DE Number: 2171533
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: free logic
zbMATH Keywords: dialogue games
zbMATH Keywords: partial logic
reviewed by: Siegfried J. Gottwald
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2171533