On elementary extensions in Fuzzy Predicate Logics

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

On elementary equivalence in fuzzy predicate logics

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. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863-880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and Cintula (J Symb Log 71(3):863-880, 2006) and of Section 4 of Cerami and Esteva (Arch Math Log 50(5/6):625-641, 2011) to non-exhaustive model

Advances on elementary equivalence in model theory of fuzzy logics

Dellunde and Garca-Cerda~na are supported by EdeTRI (TIN2012-39348-C02-01); Garca-Cerda~na is also supported by the Spanish MICINN project MTM 201125745 and the grant 2009SGR 1433 from the Generalitat de Catalunya;Noguera is supported by the project GA13-14654S of the Czech Science Foundation and by the FP7-PEOPLE-2009-IRSES project MaToMUVI (PIRSES-GA-2009-247584)Peer Reviewe

A note on many valued quantum computational logics

The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space C^3, we discuss extensions of several gates to this space and, using the notion of effect probability, we provide a characterization of its states.Comment: Pages 15, Soft Computing, 201