On Strongly Standard Complete Fuzzy Logics: MTLQ* and its Expansions

Finding strongly standard complete axiomatizations 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 paper 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 MTLalgebra expanded with additional connectives whose interpretations on [0, 1] are functions with no jump-type discontinuities. URL http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.117 [4] Source URL: https://www.iiia.csic.es/en/node/54419 Links [1] https://www.iiia.csic.es/en/staff/amanda-vidal [2] https://www.iiia.csic.es/en/staff/llu%C3%ADs-godo [3] https://www.iiia.csic.es/en/staff/francesc-esteva [4] http://dx.doi.org/10.2991/ifsa-eusflat-15.2015.117