Filters in Algebras of Fuzzy logics

0362697 - ÚI 2012 RIV NL eng C - Conference Paper (international conference)
Víta, Martin - Cintula, Petr
Filters in Algebras of Fuzzy logics.
Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology. Amsterdam: Atlantis Press, 2011 - (Galichet, S.; Montero, J.; Mauris, G.), s. 169-174. Advances in Intelligent Systems Research. ISBN 978-90-78677-00-0. ISSN 1951-6851.
[EUSFLAT - LFA 2011. Conference of the European Society for Fuzzy Logic and Technology and les Recontres Francophones sur la Logique Floue et ses Applications. Aix-Les-Bains (FR), 18.07.2011-22.07.2011]
R&D Projects: GA ČR GD401/09/H007; GA MŠMT(CZ) 1M0545
Institutional research plan: CEZ:AV0Z10300504
Keywords : filters * abstract algebraic logic * Rasiowa-implicative logics
Subject RIV: BA - General Mathematics

This paper presents a generalization of many particular results about special types of filters (e.g., (positive) implicative, fantastic) on algebras of nonclassical (mostly fuzzy) logics. Our approach is rooted in the framework of Abstract Algebraic Logic, and is based on the close connection between the filter-defining conditions and alternative axiomatizations of the logics involved. We identify four main kinds of theorems proved in the literature and we formulate general theorems which (provided a simple syntactical proof) yield the majority of published results as their direct consequences.
Permanent Link: http://hdl.handle.net/11104/0198948