On elementary equivalence in Fuzzy Predicate Logics
Publication Type:
Journal ArticleSource:
Archive for Mathematical Logic, Springer-Verlag (In Press)Keywords:
Mathematical Logic and Foundations; Model Theory; Fuzzy Predicate Logics; Elementary Extensions; Witnessed Models; Quasi-witnessed ModelsAbstract:
Our work is a contribution to the model theory of fuzzy predicate logics. In
this paper we characterize elementary equivalence between models of fuzzy predicate
logic using elementary mappings. Re ning the method of diagrams we give a solution
to an open problem of P. Hajek and P. Cintula (Conjectures 1 and 2 of [HaCi06]).
We investigate also the properties of elementary extensions in witnessed and quasiwitnessed
theories, generalizing some results of Section 7 of [HaCi06] and of Section 4
of [CeEs11] to non-exhaustive models.
Strict core fuzzy logics and quasi-witnessed models
Preserving Mappings in Fuzzy Predicate Logics
Publication Type:
Journal ArticleSource:
Journal of Logic and Computation (In Press)Keywords:
equality-free language; fuzzy predicate logic; method of diagrams; model theory; reduced structureAbstract:
In this paper we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the model-theoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts being studied are the Leibniz congruence and the structure-preserving relation. On the one hand, the Leibniz congruence of a model identifies the elements that are indistinguishable using equality-free atomic formulas and parameters from the model. A reduced structure is the quotient of a model modulo this congruence. On the other hand, the structure-preserving relation between two structures plays the same role that the isomorphism relation plays in classical predicate languages with equality.
On elementary extensions in Fuzzy Predicate Logics
Publication Type:
Conference PaperSource:
IPMU 2010, Volume 6178, Dortmund, Germany, p.747-756 (2010)Keywords:
equality-free language; fuzzy predicate logic; model theory; elementary extension; elementary equivalenceAbstract:
Abstract. Our work is a contribution to the model-theoretic study of
equality-free fuzzy predicate logics. We give a characterization of ele-
mentary equivalence in fuzzy predicate logics using elementary exten-
sions and introduce an strengthening of this notion, the so-called strong
elementary equivalence. Using the method of diagrams developed in [5]
and elementary extensions we present a counterexample to Conjectures
1 and 2 of [8].
