Prioritised Default Logic as Argumentation with Partial Order Default Priorities

TL;DR

This paper models Brewka's prioritised default logic as an argumentation framework using ASPIC+ and demonstrates that justified arguments align with PDL extensions, enabling distributed reasoning.

Contribution

It introduces a novel argumentation-based characterization of PDL with partial order priorities, extending previous total order approaches.

Findings

Arguments correspond to PDL extensions

Partial order priorities are effectively handled

Framework supports distributed non-monotonic reasoning

Abstract

We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the conclusions of the justified arguments correspond to the PDL extensions. We will first assume that the default priority is total, and then generalise to the case where it is a partial order. This provides a characterisation of non-monotonic inference in PDL as an exchange of argument and counter-argument, providing a basis for distributed non-monotonic reasoning in the form of dialogue.