Introducing Grades in Deontic Logics

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

Abstract

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.