The lexicographic closure as a revision process

TL;DR

This paper explores the relationship between nonmonotonic reasoning and belief revision by demonstrating how the lexicographic closure of defaults can be viewed as an iterated revision process, linking two important areas in logic.

Contribution

It introduces a novel perspective by conceptualizing lexicographic closure as an iterated belief revision process using Nayak’s framework.

Findings

Lexicographic closure can be modeled as a belief revision process.

The connection between default entailment and belief revision is explicitly demonstrated.

Provides a new approach to understanding nonmonotonic reasoning through belief revision.

Abstract

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing "if A is true then, normally, B is true" be said to follow from a given set of items of such information. Many answers to this question have been proposed but, surprisingly, virtually none have attempted any explicit connection to belief revision. The aim of this paper is to give an example of how such a connection can be made by showing how the lexicographic closure of a set of defaults may be conceptualised as a process of iterated revision by sets of sentences. Specifically we use the revision process of Nayak.