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On Rational Weak Nilpotent Minimum Logics
Francesc Esteva, Luis Godo and Carles Noguera

In this paper we investigate extensions of Godel 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 Godel 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 r — y, where r is y a rational in [0, 1] and y is a formula without rational truth-constants.

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