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On strongly standard complete fuzzy logics: $MTL^Q_*$ and its expansions

AuthorsVidal, Amanda; Godo, Lluis ; Esteva, Francesc
KeywordsMTL logic expansions
Strong standard completeness
Fuzzy logics
Pavelka-style completeness
Rational expansions
Infinitary logics
Issue Date30-Jun-2015
PublisherAtlantis Press
CitationProceedings IFSA-EUSFLAT,2015,pp.828-835
AbstractFinding 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 MTL-algebra expanded with additional connectives whose interpretations on [0, 1] are functions with no jump-type discontinuities.
Identifiersdoi: 10.2991/ifsa-eusflat-15.2015.117
issn: 1951-6851
isbn: 978-94-62520-77-6
Appears in Collections:(IIIA) Comunicaciones congresos
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