Another perspective on Default Reasoning

TL;DR

This paper introduces the lexicographic closure, a new rational extension of default sets that aligns with Reiter's logic of defaults but operates without non-normal defaults, supported by numerous illustrative examples.

Contribution

It defines the lexicographic closure for finite default sets, offering a rational default logic alternative to Reiter's approach that captures core intuitions.

Findings

Lexicographic closure is a rational extension of default sets.

It does not require non-normal defaults.

Examples show alignment with Reiter's logic principles.

Abstract

The lexicographic closure of any given finite set D of normal defaults is defined. A conditional assertion "if a then b" is in this lexicographic closure if, given the defaults D and the fact a, one would conclude b. The lexicographic closure is essentially a rational extension of D, and of its rational closure, defined in a previous paper. It provides a logic of normal defaults that is different from the one proposed by R. Reiter and that is rich enough not to require the consideration of non-normal defaults. A large number of examples are provided to show that the lexicographic closure corresponds to the basic intuitions behind Reiter's logic of defaults.