Adding truth-constants to logics of continuous t-norms
|Title:||Adding truth-constants to logics of continuous t-norms: axiomatization and completeness results|
|Journal:||Fuzzy Sets and Systems|
In this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Lukasiewicz 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 , for a suitable countable , and provide a full description of completeness results when (i) the t-norm is a finite ordinal sum of Lukasiewicz, 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 Lukasiewicz components behave as rational numbers.