On Rational Weak Nilpotent Minimum Logics
Authors: |
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Title: | On Rational Weak Nilpotent Minimum Logics | |||
Journal: | Journal of Multiple-Valued Logic and Soft Computing | |||
Volume | 12 | |||
Number | 1 | |||
Pages: | 9-32 | |||
Year: | 2006 | |||
Preprint |
Abstract
In this paper we investigate extensions of Gödel and Nilpotent Minimum logics by adding rational truth-values as truth constants in the language and by adding corresponding book-keeping axioms for the truth-constants. We also investigate the rational extensions of some parametric families of Weak Nilpotent Minimum logics, weaker than both Gödel and Nilpotent Minimum logics. Weak and strong standard completeness of these logics are studied in general and in particular when we restrict ourselves to formulas of the kind 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} \rightarrow \psi} , where 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 r} is a rational in 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]} and 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 \psi} is a formula without rational truth-constants.