On Lukasiewicz logic with truth-constants

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Authors:
Roberto Cignoli
Francesc Esteva
Lluís Godo
Title of the chapter: On Lukasiewicz logic with truth-constants
Title of the book: Theoretical Advances and Applications of Fuzzy Logic and Soft Computing
Editor(s):



O. Castillo
Pages: 869-875
Publisher: Springer-Verlag
City:
Year: 2007




Abstract

Canonical completeness results for L(\mathcal{C}), the expansion of Lukasiewicz logic with a countable set of truth-constants \mathcal{C}, have been recently proved for the case when the algebra of truth constants \mathcal{C} is a subalgebra of the rational interval [0, 1] \cap \mathbb{Q}. The case when C \not \subseteq [0, 1] \cap \mathbb{Q} was left as an open problem. In this paper we solve positively this open problem by showing that L(\mathcal{C}) is strongly canonical complete for finite theories for any countable subalgebra \mathcal{C} of the standard Lukasiewicz chain [0,1]L.

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