TitleIntroducing Grades in Deontic Logics
Publication TypeConference Paper
Year of Publication2008
AuthorsDellunde P, Godo L
Editorvan der Meyden R, eds.) Lvan der To
Conference NameNinth International Conference on Deontic Logic in Computer Science (DEON'08)
EditionRon van der Meyden and Leon van der Torre
Conference LocationLuxembourg
Date Published15/07/2008

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 $Φ\in SDL$, our language contains formulas of the form $\overline{r} \to NΦ$ or $\overline{r} \to PΦ$, where $r \in [0, 1]$, expressing that the preference or probability degree respectively of a norm Φ is at least $r$. We present sound and complete axiomatisations for these logics.