Avoiding Pragmatic Oddity: a bottom-up Defeasible Deontic Logic

This paper presents an extension of Defeasible Deontic Logic to deal with the Pragmatic Oddity problem. The logic applies three general principles: (i) the Pragmatic Oddity problem must be solved within a general logical treatment of contrary- to-duty (CTD) reasoning; (ii) non-monotonic methods must be adopted to handle CTD reasoning; (iii) logical models of CTD reasoning must be computationally feasible and, if possible, efficient. The proposed extension of Defeasible Deontic Logic elaborates a preliminary version of the model proposed by Governatori and Rotolo [15]. The previous solution was based on particular characteristics of the (constructive, top-down) proof theory of the logic. However, that method introduces some degree of non-determinism. To avoid the problem, we provide a bottom-up characterization of the logic. The new characterization offers insights for the efficient implementation of the logic and allows us to establish the computational complexity of the problem.