Deontic Meta-Rules

TL;DR

This paper extends non-monotonic logic frameworks to include deontic aspects, enabling modeling of policies and legal systems, and introduces efficient algorithms for reasoning with defeasible deontic meta-rules.

Contribution

It formalizes two variants of Defeasible Deontic Logic with Meta-Rules and develops algorithms to compute their extensions, addressing computational properties of such theories.

Findings

Formalization of defeasible meta-theories with deontic modalities

Introduction of conflict types in defeasible deontic logic

Development of efficient algorithms for extension computation

Abstract

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) 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 (DL) 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 with Meta-Rules to represent (1) defeasible meta-theories with deontic modalities, and (2) two different types of conflicts among rules: Simple Conflict Defeasible Deontic Logic, and Cautious Conflict Defeasible Deontic Logic. Second, we advance efficient algorithms to compute the extensions for both variants.