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

This paper focuses on completeness results about generic expansions of propositional Weak Nilpotent Minimum (WNM) logics 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) the t-norm is a Weak Nilpotent Minimum satisfying the finite partition property and (ii) the set of truth-constants covers all the unit interval in the sense that each interval of the partition contains values of C in its interior.