Ordering-based Representations of Rational Inference

TL;DR

This paper characterizes rational inference relations using total preorders of formulas and introduces an application-oriented representation based on graded consequence operators, extending existing frameworks.

Contribution

It provides a new simple characterization of rational inference relations via total preorders and introduces a practical representation using graded consequence operators.

Findings

Characterization of rational inference relations with total preorders.

Extension of Gardenfors and Makinson's results for expectation inference.

Application-oriented representation using graded consequence operators.

Abstract

Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original representation by preferential models. In this paper, we shall characterize them with a class of total preorders of formulas by improving and extending Gardenfors and Makinson's results for expectation inference relations. A second representation is application-oriented and is obtained by considering a class of consequence operators that grade sets of defaults according to our reliance on them. The finitary fragment of this class of consequence operators has been employed by recent default logic formalisms based on maxiconsistency.