Handbook of philosophical logic. Vol. 6
This volume contains four chapters. The first two of them, ``Relevance logic'' by \textit{J. M. Dunn} and \textit{G. Restall} (pp. 1--128) and ``Quantum logics'' by \textit{M.-L. Dalla Chiara} and \textit{R. Giuntini} (pp. 129--228), are updated versions of corresponding chapters of the first authors, respectively, in Vol.~3 of the first edition. The chapter on relevance logic has been slightly updated and extended at different places. Additionally, it contains a new final section, ``Looking about'', intended to mention (some) strategic directions of recent research. It discusses Dunn's gaggle theory, Belnap's display logic, paraconsistency, semantic neighbours, and relevant predication. The quantum logics chapter was considerably expanded and updated. It covers now also matters like effect algebras, unsharp approaches, Brouwer-Zadeh algebras, and sequent calculi. The other two chapters survey topics which did not have separate chapters in the first edition. Chapter 3 on ``Combinators, proofs, and implicational logics'' (pp. 229--286), written by \textit{M. Bunder}, starts with the basic facts about combinatory logic and the \(\lambda\)-calculus, soon introduces types, and has its focus (i) on the formulas-as-types isomorphism, also known as Curry-Howard isomorphism, which relates combinations of basic combinators or \(\lambda\)-terms with proofs in intuitionistic implicational logic, and (ii) to a large extent on generalizations of these considerations to other logics. The final chapter, ``Paraconsistent logic'' (pp. 287--393) by \textit{G. Priest}, covers another topic which has not been present in the first edition. The author surveys the most important approaches toward logical systems which are ``tolerant'' w.r.t. contradictions, with emphasis more -- but not exclusively -- on the logical than on the philosophical side, including paraconsistent set theory and arithmetic. He (successfully) tries to give a fair representation of the different, and sometimes competing, approaches toward this topic. A final section is devoted to philosophical problems around and applications of paraconsistency.
scientific article; zbMATH DE number 2171534