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 $\{ \overline{r} \mid r \in C \}$, for a suitable countable $C \subseteq [0, 1]$, and provide a full description of completeness results when (i) the t-norm is a Weak Nilpotent Minimum satisfying the {\em finite partition property} and (ii) the set of truth-constants {\em covers} all the unit interval in the sense that each interval of the partition contains values of $C$ in its interior.