An Attempt to Adapt a Logic of Conditional Preferences for Reasoning with Contrary-To-Duties

This paper presents some preliminary work which attempts to adapt, in the context of deontic reasoning, the CO logic deened by Boutilier for reasoning with conditional preferences. The rst motivation for this work is that deontic logic can be given a semantics in terms of ordered worlds as in CO logic: the preference relation among worlds aims at ordering worlds from the most ideal ones to the least ideal ones. The second motivation is that Boutilier introduced a model of an agent's ability by distinguishing between controllable, innuenceable and uninnuenceable propositions. And we noticed that this partition can be related to the notions introduced by Carmo and Jones for reasoning with Contrary-To-Duties. This present work shows an extension of Boutilier's work in order to use CO logic for reasoning with Contrary-To-Duties. The results obtained with this extension do not coincide exactly with those obtained by Carmo and Jones: the full impact of these diierences has not yet been studied.