Filters in Algebras of Fuzzy logics

Authors: Martin Víta, Petr Cintula
Publication year: 2011
Publication type: Konferenční příspěvek (mezinárodní konf.)
Periodical: Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology
Projects: Logical foundations of semantics
Institute for Theoretical Computer Science
Bibliographic citation: VÍTA, Martin, CINTULA, Petr. Filters in Algebras of Fuzzy logics. In: GALICHET, S., MONTERO, J., MAURIS, G., eds. Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology. Amsterdam: Atlantis Press, 2011, S. 169-174. Advances in Intelligent Systems Research. ISBN 978-90-78677-00-0. ISSN 1951-6851
Dostupné z: doi:10.2991/eusflat.2011.123
DOI: 10.2991/eusflat.2011.123
ID: 362697

Abstract

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.