On elementary extensions in Fuzzy Predicate Logics

Abstract

10 páginas.-- Comunicación presentada a la International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU) celebrada en Dortmund (Alemania) del 28 de Junio al 2 de Julio de 2010.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].Research partially funded by the spanish projects CONSOLIDER (CSD2007- 0022), MULOG2 (TIN2007-68005-C04-01) and ARINF (TIN2009-14704-C03-03) by the ESF Eurocores-LogICCC/MICINN project FFI2008-03126- E/FILO and by the Generalitat de Catalunya under the grants 2009-SGR 1433 and 1434.Peer reviewe