@article {5067,
title = {Applications of ultraproducts: from compactness to fuzzy elementary classes},
journal = {Logic Journal of the IGPL},
volume = {22},
year = {2014},
chapter = {166},
keywords = {mathematical fuzzy logic, model theory, Ultraproducts},
author = {Pilar Dellunde}
}
@article {4686,
title = {On elementary equivalence in Fuzzy Predicate Logics},
journal = {Archive for Mathematical Logic},
volume = {52},
year = {2013},
pages = {1-17},
publisher = {Springer-Verlag},
abstract = {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. Rening 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.},
keywords = {Elementary Extensions, fuzzy predicate logics, Mathematical Logic and Foundations, model theory, Quasi-witnessed Models, Witnessed Models},
author = {Pilar Dellunde and Francesc Esteva}
}
@article {3816,
title = {Preserving Mappings in Fuzzy Predicate Logics},
journal = {Journal of Logic and Computation},
volume = {22},
year = {2012},
pages = {1367-1389},
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.},
keywords = {equality-free language, fuzzy predicate logic, method of diagrams, model theory, reduced structure},
author = {Pilar Dellunde}
}
@conference {3773,
title = {On elementary extensions in Fuzzy Predicate Logics},
booktitle = {IPMU 2010},
volume = {6178},
year = {2010},
month = {28/06/2010},
pages = {747-756},
address = {Dortmund, Germany},
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].},
keywords = {elementary equivalence, elementary extension, equality-free language, fuzzy predicate logic, model theory},
author = {Pilar Dellunde and Francesc Esteva},
editor = {E. Huellermeier, R. Kruse, and F. Hoffmann}
}