Strict core fuzzy logics and quasi-witnessed models

Abstract

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M. C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with Δ, and Δ-quasi-witnessed axioms are complete with respect to Δ-quasi-witnessed models. © 2011 Springer-Verlag.The authors acknowledge partial support of E.U. Eurocores-ESF/FWF grant I143-G15 (LogICCC-LoMoReVI), Spanish projects MULOG2 TIN2007-68005-C04-01/04, ARINF TIN2009-14704-C03-03, “Agreement Technologies” (CONSOLIDER CSD 2007-0022, INGENIO 2010) and the Generalitat de Catalunya under the grant 2009-SGR-1434. The first author is supported by grant JAEPre-doc, n.074 from CSIC.Peer Reviewe