fuzzy predicate logic

Strict core fuzzy logics and quasi-witnessed models

Publication Type:

Journal Article

Authors:

Marco Cerami; Francesc Esteva

Source:

Archive for Mathematical Logic, Volume 50, Issue 5-6, p.625-641 (2011)

Revisiting ultraproducts in fuzzy predicate logics

Publication Type:

Journal Article

Authors:

Pilar Dellunde

Source:

Journal of Multiple-Valued Logic and Soft Computing, Volume 19, Issue 1-3, p.95-108 (2012)

Keywords:

Fuzzy Predicate Logic; Ultraproducts

First-order SMTL Logic and quasi-witnessed models

Publication Type:

Conference Paper

Authors:

Marco Cerami; Francesc Esteva

Source:

XV Congreso Español sobre Tecnologías y Lógica Fuzzy ESTYLF 2010, Huelva, p.145-150 (2010)

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.

On elementary extensions in Fuzzy Predicate Logics

Publication Type:

Conference Paper

Authors:

Pilar Dellunde; Francesc Esteva

Source:

IPMU 2010, Volume 6178, Dortmund, Germany, p.747-756 (2010)

Keywords:

equality-free language; fuzzy predicate logic; model theory; elementary extension; elementary equivalence

Abstract:

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].

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