On expansions of t-norm based logics with truth-constants

This paper focuses on completeness results about generic expansions of logics of both continuous t-norms and Weak Nilpotent Minimum (WNM) with truth-constants. Indeed, we consider algebraic semantics for expansions of these logics 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) either the t-norm is a finite ordinal sum of Lukasiewicz, Gödel and Product components (and hence continuous) or the t-norm is a Weak Nilpotent Minimum with a finite partition and (ii) the set of truth-constants covers all the unit interval in the sense that each component (in case of continuous t-norm) or each interval of the partition (in the WNM case) contains values of C in its interior. Results on expansions of the logic of a continuous t-norm were already published, while many of the results about WNM are presented here for the first time.