On expansions of WNM t-norm based logics with truth-constants
Authors: |
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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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \{ \overline{r} \mid r \in C \}} , for a suitable countable Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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.