In this paper we investigate the 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. Weak and strong standard completeness of these logics are studied in general and when we restrict ourselves to formulas of the kind $overline{r} o arphi$, where $r$ is a rational in [0, 1] and $arphi$ is a formula without rational truth-constants.
Esteva, F., Godo, L., NOGUERA CLOFENT, C. (2004). On Rational Gödel and Nilpotent Minimum Logics. In Tenth international conference IPMU 2004, Information processing and management of uncertainty in knowledge-based systems (pp.561-568). Perugia : Casa editrice Università La Sapienza.
On Rational Gödel and Nilpotent Minimum Logics
Carles Noguera Clofent
2004-01-01
Abstract
In this paper we investigate the 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. Weak and strong standard completeness of these logics are studied in general and when we restrict ourselves to formulas of the kind $overline{r} o arphi$, where $r$ is a rational in [0, 1] and $arphi$ is a formula without rational truth-constants.
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https://hdl.handle.net/11365/1201023