Prohairetic deontic logic (PDL)

Abstract

In this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based dyadic deontic logic. An obligation ‘α should be (done) if β is (done)’ is true if (1) no ¬α^β state is as preferable as an α^β state and (2) the preferred β states are α states. We show that the different elements of this mixed representation solve different problems of deontic logic. The first part of the deffnition is used to formalize contrary-toduty reasoning, that for example occurs in Chisholm’s and Forrester’s notorious deontic paradoxes. The second part is used to make dilemmas inconsistent. PDL shares the intuitive semantics of preference-based deontic logics without introducing additional semantic machinery such as bi-ordering semantics or ceteris paribus preferences.