Handbook of philosophical logic. Vol. 5
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.
scientific article; zbMATH DE number 2171533