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.
Esteva, F., Godo, L., NOGUERA CLOFENT, C. (2004). On Rational Weak Nilpotent Minimum Logics. In Actas del XII congreso español sobre tecnologías y lógica fuzzy ESTYLF 2004 (pp.413-418). Jaén : Universidad de Jaén.
On Rational Weak Nilpotent Minimum Logics
Carles Noguera Clofent
2004-01-01
Abstract
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.
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https://hdl.handle.net/11365/1201021