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

Authors:
Francesc Esteva;Lluís Godo;Carles Noguera
Affiliations:
Artificial Intelligence Research Insitute (IIIA) - CSIC, Campus de la Universitat Autònoma de Barcelona s/n, 08193 Bellaterra, Catalonia, Spain;Artificial Intelligence Research Insitute (IIIA) - CSIC, Campus de la Universitat Autònoma de Barcelona s/n, 08193 Bellaterra, Catalonia, Spain;Department of Mathematics and Computer Science, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy
Venue:
Fuzzy Sets and Systems
Year:
2010

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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 {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.