Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
Issue date
2007Author
Noguera, Carles
Esteva, Francesc
Gispert, Joan
Godó, Lluís
Metadata
Show full item recordAbstract
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.