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

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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.