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Title:
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Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
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Author:
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Noguera, Carles; Esteva, Francesc; Gispert, Joan; Godó, Lluís
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Notes:
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In 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 {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.
Esteva, Godo and Noguera acknowledge partial support of the Spanish project MULOG TIN2004-07933-C03- 01. Gispert acknowledges partial support to the projects MULOG TIN2004-07933-C03-02, 2005SGR00083 and MTM2004-031012001-3329. |
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Subject(s):
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-Basic fuzzy logic BL
-Gödel
-Łukasiewicz and product logics
-T-norm-based logic |
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Rights:
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(c) Elsevier B.V., 2007
info:eu-repo/semantics/restrictedAccess |
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Document type:
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article
publishedVersion |
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Published by:
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Elsevier
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