Publications

Preserving Mappings in Fuzzy Predicate Logics

Publication Type:

Journal Article

Authors:

Pilar Dellunde

Source:

Journal of Logic and Computation (In Press)

Keywords:

equality-free language; fuzzy predicate logic; method of diagrams; model theory; reduced structure

Abstract:

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.

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