Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
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Date
2007
Authors
Noguera, Carles
Esteva, Francesc
Gispert, Joan
Godó, Lluís
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Abstract
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.
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Fuzzy Sets and Systems, 2007, vol. 158, núm. 6, p. 597-618