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Title

Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results

AuthorsEsteva, Francesc ; Gispert, Joan; Godo, Lluis ; Noguera, Carles
KeywordsŁukasiewicz and product logics
T-norm-based logic
Expansions with truth-constants
Gödel
Rational pavelka logic
Standard completeness
Basic fuzzy logic BL
Issue Date2007
PublisherElsevier
CitationFuzzy Sets and Systems 158: 597- 618 (2007)
AbstractIn this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Łukasiewicz logic and more recent results for Gödel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants { over(r, -) | r ∈ C }, for a suitable countable C ⊆ [0, 1], and provide a full description of completeness results when (i) the t-norm is a finite ordinal sum of Łukasiewicz, Gödel and Product components, (ii) the set of truth-constants covers all the unit interval in the sense that each component of the t-norm contains at least one value of C different from the bounds of the component, and (iii) the truth-constants in Łukasiewicz components behave as rational numbers. © 2007 Elsevier B.V. All rights reserved.
URIhttp://hdl.handle.net/10261/159904
Identifiersdoi: 10.1016/j.fss.2006.11.010
issn: 0165-0114
Appears in Collections:(IIIA) Artículos
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