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.
Links:
[1] http://www.iiia.csic.es/en/individual/pilar-dellunde
[2] http://www.iiia.csic.es/en/publications/keyword/equality-free language
[3] http://www.iiia.csic.es/en/publications/keyword/fuzzy predicate logic
[4] http://www.iiia.csic.es/en/publications/keyword/method of diagrams
[5] http://www.iiia.csic.es/en/publications/keyword/model theory
[6] http://www.iiia.csic.es/en/publications/keyword/reduced structure
[7] http://www.iiia.csic.es/en/publications/export/tagged/3816
[8] http://www.iiia.csic.es/en/publications/export/xml/3816
[9] http://www.iiia.csic.es/en/publications/export/bib/3816
[10] http://www.iiia.csic.es/en/project/arinf
[11] http://www.iiia.csic.es/en/project/at
[12] http://www.iiia.csic.es/en/project/locomotion-0