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.