Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

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

Authors
Amanda Vidal, Lluis Godo, Francesc Esteva
Corresponding Author
Amanda Vidal
Available Online June 2015.
DOI
https://doi.org/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/).

Download article (PDF)

Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.117How to use a DOI?
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/).

Cite this article

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  - https://doi.org/10.2991/ifsa-eusflat-15.2015.117
ID  - Vidal2015/06
ER  -