Two-Dimensional Belief Change

ABSTRACT: In this paper I present the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is similar to the model of ‘revision by comparison’ investigated by Ferm´e and Rott (Artificial Intelligence 157, 2004). In contrast to the latter, however, bounded revision satisfies the AGM axioms as well as the Darwiche-Pearl axioms. Two onedimensional special cases are obtained by setting one argument of the two-dimensional revision operation to certain extremal values. Bounded revision thus fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I argue that two-dimensional revision operations add decisively to the expressive power of qualitative approaches that refrain from assuming numbers as measures of degrees of belief.

• Type: Conference
• Year: 2007
• Where: DAGSTUHL
• Authors: Hans Rott
• Keywords: DAGSTUHL 2007, Software Engineering, Two-dimensional Revision, Two-dimensional Revision Functions, Two-dimensional Revision Operations