On Rational Weak Nilpotent Minimum Logics
Francesc Esteva, Lluı́s Godo, Carles Noguera · 2004
In this paper we investigate some extensions of Weak Nilpotent Minimum logic, a weaker logic than both 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. Weak and strong standard completeness of these logics are studied in general and when we restrict ourselves to formulas of the kind r → φ, where r is a rational in [0, 1] and φ is a formula without rational truth-constants.