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

DOI

10.2991/ifsa-eusflat-15.2015.117How to use a DOI?

Keywords

Fuzzy logics, Strong standard completeness, MTL logic expansions, rational expansions, Pavelka-style completeness, infinitary logics.

Abstract

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 MTL-algebra expanded with additional connectives whose interpretations on [0, 1] are functions with no jump-type discontinuities.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Amanda Vidal
AU  - Lluis Godo
AU  - Francesc Esteva
PY  - 2015/06
DA  - 2015/06
TI  - On Strongly Standard Complete Fuzzy Logics: MTLQ* and its Expansions.
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 828
EP  - 835
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.117
DO  - 10.2991/ifsa-eusflat-15.2015.117
ID  - Vidal2015/06
ER  -