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].
