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 { 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.
Esteva, F., Gispert, J., Godo, L., Noguera, C. (2007). Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results. FUZZY SETS AND SYSTEMS, 158(6), 597-618 [10.1016/j.fss.2006.11.010].
Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
Noguera C.
2007-01-01
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 { 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.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1200742