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

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Issue date
2007
Author
Noguera, Carles
Esteva, Francesc
Gispert, Joan
Godó, Lluís
Suggested citation
Noguera, Carles; Esteva, Francesc; Gispert, Joan; Godó, Lluís; . (2007) . Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results. Fuzzy Sets and Systems, 2007, vol. 158, núm. 6, p. 597-618. https://doi.org/10.1016/j.fss.2006.11.010.
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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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http://hdl.handle.net/10459.1/57375
DOI
https://doi.org/10.1016/j.fss.2006.11.010
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Fuzzy Sets and Systems, 2007, vol. 158, núm. 6, p. 597-618
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