Deontic meta-rules

The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions of such theories were proposed in Olivieri et al. (2021, Computing defeasible meta-logic. In JELIA 2021, LNCS, vol. 12678, pp. 69-84. Springer.). This work extends such a logical framework by considering the deontic aspect. The resulting logic will not just be able to model policies but also tackle well-known aspects that occur in numerous legal systems. The use of Defeasible Logic to model meta-rules in the application area we just alluded to has been investigated. Within this line of research, the study mentioned above was not focusing on the general computational properties of meta-rules.This study fills this gap with two major contributions. First, we introduce and formalise two variants of Defeasible Deontic Logic (DDL) with meta-rules to represent (i) defeasible meta-theories with deontic modalities and (ii) two different types of conflicts among rules: Simple Conflict DDL and Cautious Conflict DDL. Second, we advance efficient algorithms to compute the extensions for both variants.