Introducing Grades in Deontic Logics

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Pilar Dellunde
Lluís Godo
Title: Introducing Grades in Deontic Logics
Journal: Lecture Notes in Computer Science
Volume 5076
Pages: 248-262
Year: 2008


In this paper we define a framework to introduce gradedness in Deontic logics through the use of fuzzy modalities. By way of example, we instantiate the framework to Standard Deontic logic (SDL) formulas. Given a deontic formula $ \Phi\in SDL $, our language contains formulas of the form $ \overline{r}\to N\Phi $ or $ \overline{r} \to P\Phi $, where $ r \in [0, 1] $, expressing that the preference or probability degree respectively of a norm $ \Phi $ is at least $ r $. We present sound and complete axiomatisations for these logics.