Handbook of mathematical fuzzy logic. Volume 2 (Q2871198)

This handbook consists of two volumes (a third volume is in preparation), for Volume 1 see [Zbl 1283.03001].NEWLINENEWLINE Volume 2 starts with the fundamental aspects of MV-algebra theory and Łukasiewicz logic, given as a self-contained text (``Łukasiewicz logic and MV-algebras'' (pp. 469--583) by \textit{Antonio Di Nola} and \textit{Ioana Leuştean}). An overview of Gödel logics, including the corresponding first-order predicate calculi, Kripke semantics and axiomatizability results, is also presented (``Gödel-Dummett logics'' (pp. 585--625) by \textit{Matthias Baaz} and \textit{Norbert Preining}). Problems related to the expressive power of language are discussed with a detailed analysis of language expansions (``Fuzzy logics with enriched language'' (pp. 627--711) by \textit{Francesc Esteva}, \textit{Lluís Godo} and \textit{Enrico Marchioni}). The concrete representations of free algebras in varieties constituting the equivalent algebraic semantics of some prominent schematic extensions of basic logic and monoidal t-norm logic are considered (``Free algebras and functional representation for fuzzy logics'' (pp. 713--791) by \textit{Stefano Aguzzoli}, \textit{Simone Bova} and \textit{Brunella Gerla}). One chapter deals with the computational complexity of decision problems in propositional fuzzy logics and in algebras which constitute their algebraic semantics (``Computational complexity of propositional fuzzy logics'' (pp. 793--851) by \textit{Zuzana Haniková}). This volume concludes with several results regarding the complexity of predicate fuzzy logics understood as first-order versions of core propositional fuzzy logics (``Arithmetical complexity of first-order fuzzy logics'' (pp. 853--908) by \textit{Petr Hájek}, \textit{Franco Montagna} and \textit{Carles Noguera}).