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On completeness results for predicate lukasiewicz, product, gödel and nilpotent minimum logics expanded with truth-constants
dc.contributor.author | Esteva Massaguer, Francesc |
dc.contributor.author | Godo, L. |
dc.contributor.author | Noguera, C. |
dc.date.accessioned | 2011-10-14T16:08:56Z |
dc.date.available | 2011-10-14T16:08:56Z |
dc.date.issued | 2007 |
dc.identifier.citation | Esteva Massaguer, Francesc; Godo, L.; Noguera, C. On completeness results for predicate lukasiewicz, product, gödel and nilpotent minimum logics expanded with truth-constants. "Mathware & Soft Computing", 2007, vol. 14, núm. 3, p. 233-246. |
dc.identifier.issn | 1134-5632 |
dc.identifier.uri | http://hdl.handle.net/2099/10931 |
dc.description.abstract | In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completeness results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics with truth-constants are conservative, which already implies the failure of standard completeness for the case of Product logic. In contrast, the expansions of predicate Gödel and Nilpotent Minimum logics are proved to be strong standard complete but, when the semantics is restricted to the canonical algebra, they are proved to be complete only for tautologies. Moreover, when the language is restricted to evaluated formulae we prove canonical completeness for deductions from finite sets of premises. |
dc.format.extent | 14 p. |
dc.language.iso | eng |
dc.publisher | Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica |
dc.relation.ispartof | Mathware & Soft Computing. 2007, vol. 14, núm. 3 |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Lògica matemàtica |
dc.subject.lcsh | Logic, symbolic and mathematical |
dc.subject.other | Monoidal t-norm based logic |
dc.subject.other | Core predicate fuzzy logics |
dc.subject.other | Rational Pavelka logic |
dc.subject.other | Gödel and nilpotent minimum predicate logics |
dc.subject.other | Expansions with truth-constants |
dc.subject.other | Completeness results |
dc.title | On completeness results for predicate lukasiewicz, product, gödel and nilpotent minimum logics expanded with truth-constants |
dc.type | Article |
dc.subject.lemac | Lògica matemàtica |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::03 Mathematical logic and foundations::03B General logic |
dc.rights.access | Open Access |
local.citation.author | Esteva Massaguer, Francesc; Godo, L.; Noguera, C. |
local.citation.publicationName | Mathware & Soft Computing |
local.citation.volume | 14 |
local.citation.number | 3 |
local.citation.startingPage | 233 |
local.citation.endingPage | 246 |
local.ordre | 5 |