In this paper we introduce Prohairetic Deontic Logic, a preference-based dyadic deontic logic. An obligation `ff should be (done) if fi is (done)' is true if (1) no :ff fi is preferred to an fffi and (2) the preferred fi are ff. We show that this mixed representation solves several problems of deontic logic. Moreover, we discuss the relation between preferencebased deontic logic and qualitative decision theory. Introduction Deontic logic is a modal logic developed in philosophical logic. Absolute and conditional obligations are represented by the modal formulas Off and O(ff j fi), where the latter is read as `ff ought to be (done) if fi is (done).' The development of preference-based deontic logic is plagued by the following three (related) problems: Strong preference problem. Preferences for ff 1 and ff 2 conflict for ff 1 :ff 2 and :ff 1 ff 2 . Contrary-to-duty problem. A contrary-to-duty obligation is an obligation that refers to a sub-ideal situation. Reasoning structures lik..
