TitleOn strongly standard complete fuzzy logics: MTL^Q_*and its expansions
Publication TypeConference Paper
Year of Publication2015
AuthorsVidal A, Godo L, Esteva F
Conference NameProc. of the Joint Conference IFSA-EUSFLAT 2015
EditionJ.M. Alonso et al.
PublisherAtlantis Press
Conference LocationGijón, Spain
Pagination828-835
Date Published30/06/2015
Abstract

Finding strongly standard complete axiomatiza- tions for t-norm based fuzzy logics (i.e. complete for deductions with infinite sets of premises w.r.t. semantics on the real unit interval [0, 1]) is still an open problem in general, even though results are already available for some particular cases like some infinitary logics based on a continuous t-norm or certain expansions of Monoidal t-norm based logic (MTL) with rational constant symbols. In this pa- per we propose a new approach towards the problem of defining strongly standard complete for logics with rational constants in a simpler way. We present a method to obtain a Hilbert-Style axiomatization of the logic associated to an arbitrary standard MTL-algebra expanded with additional connectives whose interpretations on [0, 1] are functions with no jump-type discontinuities.

URLhttp://dx.doi.org/10.2991/ifsa-eusflat-15.2015.117