Representation Theory for Default Logic

TL;DR

This paper investigates how families of belief theories can be represented using default logic, providing a complete characterization for normal default theories and exploring the limits of representability.

Contribution

It offers a complete solution for representability with normal default theories and partial results for arbitrary default theories, including non-representability examples.

Findings

Complete characterization of representability with normal default theories

Partial results on representability by arbitrary default theories

Examples of non-representable families of theories

Abstract

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the representability by means of normal default theories. We obtain partial results on representability by arbitrary default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories.