Adding truth-constants to logics of continuous t-norms: Axiomatization and completeness results
In this paper we study generic expansions of logics of continuous t-norms with truth-constants, taking advantage of previous results for Lukasiewicz logic and more recent results for Godel and Product logics. Indeed, we consider algebraic semantics for expansions of logics of continuous t-norms with a set of truth-constants {(r) over bar vertical bar r is an element of C}, for a suitable countable C subset of [0, 1], and provide a full description of completeness results when (i) the t-norm is a finite ordinal sum of Lukasiewicz, Godel and Product components, (ii) the set of truth-constants covers all the unit interval in the sense that each component of the t-norm contains at least one value of C different from the bounds of the component, and (iii) the truth-constants in Lukasiewicz components behave as rational numbers. (C) 2006 Elsevier B.V. All rights reserved.
godel basic fuzzy logic bl lukasiewicz and product logics t-norm-based logic expansions with truth-constants rational pavelka logic standard completeness