Distinguished Algebraic Semantics for t-norm Based Fuzzy Logics: Methods and Algebraic Equivalencies

Autoři: doc. Ing. Petr Cintula, Ph.D. DSc.
Rok vydání: 2009
Typ publikace: Článek v odborném periodiku
Periodikum: Annals of Pure and Applied Logic
Projekty: Institut Teoretické Informatiky
Bibliografická citace: CINTULA, Petr, ESTEVA, F., GISPERT, J., GODO, L., MONTAGNA, F., NOGUERA, C. Distinguished Algebraic Semantics for t-norm Based Fuzzy Logics: Methods and Algebraic Equivalencies. Annals of Pure and Applied Logic. 2009, 160(1), 53-81. ISSN 0168-0072. E-ISSN 1873-2461
Dostupné z: doi:10.1016/j.apal.2009.01.012
DOI: 10.1016/j.apal.2009.01.012
ID: 323929

Abstrakt

This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Delta-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics, study their relationships, characterization and we survey the known completeness methods and results for prominent logics. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved.