Permissions and Uncontrollable Propositions in DSDL3: Non-monotonicity and Algorithms

In this paper we are interested in non-monotonic extensions of Bengt Hansson’s standard dyadic deontic logic 3, known as DSDL3. We study specificity principles for DSDL3 with both controllable and uncontrollable propositions. We introduce an algorithm for minimal specificity which not only covers obligations but also permissions, and we discuss the distinction between weak and strong permissions. Moreover, we introduce ways to combine algorithms for minimal and maximal specificity for DSDL3 with controllable and uncontrollable propositions, based on ‘optimistic’ and ‘pessimistic’ reasoning respectively.