Abstract:

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.

Notes:

This paper is an updated and shortened version of the manuscript "On expansions of t-norm based logics with truth-constants'' that was written in 2006 as a kind of survey, but also with new results and proofs, in principle intended to appear in a book gathering contributions presented at the Linz Seminar 2005 but eventually never edited. Since then, new developments on this topic have been published \cite{egn09sc,egn09apal} using or referring to results from this paper. Although it might be felt as a sort of circular referencing, for the sake of being  complete, we will also refer to them when appropriate.

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