On elementary equivalence in Fuzzy Predicate Logics
Publication Type:
Journal ArticleSource:
Archive for Mathematical Logic, Springer-Verlag (In Press)Keywords:
Mathematical Logic and Foundations; Model Theory; Fuzzy Predicate Logics; Elementary Extensions; Witnessed Models; Quasi-witnessed ModelsAbstract:
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. Re ning 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.
Revisiting Ultraproducts in Fuzzy Predicate Logics
Publication Type:
Conference PaperSource:
40th IEEE International Symposium on Multiple-Valued Logic, IEEE Computer Society, Barcelona, p.134-139 (2010)ISBN:
978-0-7695-4024-5Keywords:
ultraproducts; reduced products; fuzzy predicate logics; reduced semanticsAbstract:
In this paper we examine different possibilities of defining reduced products and ultraproducts in fuzzy predicate logics. We present analogues to the Los Theorem for these notions and discuss the advantages and drawbacks of each definition introduced. Following the work in [De09], we show that these constructions are adequate for working in a reduced semantics.
Notes:
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