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dc.contributor.authorEsteva, Francesc-
dc.contributor.authorGodo, Lluis-
dc.contributor.authorNoguera, Carles-
dc.date.accessioned2018-02-09T15:29:25Z-
dc.date.available2018-02-09T15:29:25Z-
dc.date.issued2009-
dc.identifierdoi: 10.1016/j.apal.2009.05.014-
dc.identifierissn: 0168-0072-
dc.identifier.citationAnnals of Pure and Applied Logic 161: 185- 202 (2009)-
dc.identifier.urihttp://hdl.handle.net/10261/160427-
dc.description.abstractThis paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms (mainly continuous and weak nilpotent minimum t-norms). We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical real and rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind over(r, -) → φ, where φ has no additional truth-constants. © 2009 Elsevier B.V. All rights reserved.-
dc.description.sponsorshipThe authors acknowledge partial support of the Spanish project MULOG2 (TIN2007-68005-C04), including feder funds of the European Union, and by the Agreement Technologies CONSOLIDER CSD2007-0022, INGENIO 2010 and the ESF Eurocores-LogICCC/MICINN project FFI2008-03126-E/FILO. The third author also acknowledges partial support from the grant 2006-BP-A-10043 of the Departament d’Educació i Universitats of the Generalitat de Catalunya. We are indebted with professor Petr Hájek for his helpful remarks about conservative expansions, and with the anonymous referees whose reports helped in improving the paper a lot.-
dc.publisherElsevier-
dc.relation.isversionofPostprint-
dc.rightsopenAccess-
dc.subjectTruth-constants-
dc.subjectT-norm based fuzzy logics-
dc.subjectResiduated lattices-
dc.subjectMathematical fuzzy logic-
dc.subjectFirst-order predicate non-classical logics-
dc.subjectAlgebraic logic-
dc.titleFirst-order t-norm based fuzzy logics with truth-constants: Distinguished semantics and completeness properties-
dc.typeartículo-
dc.identifier.doihttp://dx.doi.org/10.1016/j.apal.2009.05.014-
dc.date.updated2018-02-09T15:29:26Z-
dc.description.versionPeer Reviewed-
dc.language.rfc3066eng-
dc.contributor.funderMinisterio de Economía y Competitividad (España)-
dc.contributor.funderGeneralitat de Catalunya-
dc.contributor.funderEuropean Geosciences Union-
dc.relation.csic-
dc.identifier.funderhttp://dx.doi.org/10.13039/501100001649es_ES
dc.identifier.funderhttp://dx.doi.org/10.13039/501100002809es_ES
dc.identifier.funderhttp://dx.doi.org/10.13039/501100003329es_ES
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