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

Authors:	Francesc Esteva Lluís Godo Carles Noguera
Title:	On expansions of WNM t-norm based logics with truth-constants
Journal:	Fuzzy Sets and Systems
Volume	161
Number	3
Pages:	347-368
Year:	2010
Preprint

Abstract

This paper is a summary of completeness results about generic expansions of logics of both Weak Nilpotent Minimum (WNM) and continuous t-norms 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) 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.