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On completeness results for predicate lukasiewicz, product, gödel and nilpotent minimum logics expanded with truth-constants

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Esteva Massaguer, Francesc
Godo, L.
Noguera, C.
Document typeArticle
Defense date2007
PublisherUniversitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
This work is protected by the corresponding intellectual and industrial property rights. Except where otherwise noted, its contents are licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
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.
CitationEsteva 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. 
URIhttp://hdl.handle.net/2099/10931
ISSN1134-5632
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