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 LFailed 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 (\mathcal{C})} , the expansion of Lukasiewicz logic with a countable 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 \mathcal{C}} , have been recently proved for the case when the algebra 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 \mathcal{C}} is a subalgebra of the rational interval 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 [0, 1] \cap \mathbb{Q}} . The case when 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 \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 LFailed 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 (\mathcal{C})} is strongly canonical complete for finite theories for any countable subalgebra 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 \mathcal{C}} of the standard Lukasiewicz chain 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 [0,1]_{L}} .