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

Noguera, Carles; Esteva, Francesc; Gispert, Joan; Godó, Lluís

doi:https://doi.org/10.1016/j.fss.2006.11.010

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Issue date

2007

Author

Noguera, Carles

Esteva, Francesc

Gispert, Joan

Godó, Lluís

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.

URI

http://hdl.handle.net/10459.1/57375

DOI

https://doi.org/10.1016/j.fss.2006.11.010

Is part of

Fuzzy Sets and Systems, 2007, vol. 158, núm. 6, p. 597-618