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Value-based Contraction: A Representation Horacio Arl-Costa and Hailin Liu

Summary: Value-based Contraction: A Representation
Horacio Arló-Costa and Hailin Liu
December 26, 2010
Sven-Ove Hansson and Erik Olsson studied in [7] the logical properties of
an operation of contraction first proposed by Isaac Levi in [10]. They provided
a completeness result for the simplest version of contraction that they call Levi-
contraction but left open the problem of characterizing axiomatically the more
complex operation of value-based contraction or saturatable contraction. In this
paper we propose an axiomatization for this operation and prove a completeness
result for it. We argue that the resulting operation is better behaved than various
rival operations of contraction defined in recent years.
1 Introduction
Willard Van Orman Quine pointed out in Two Dogmas of Empiricism that when we
engage in the reevaluation of a system of beliefs as a result of a recalcitrant experience
we have `[...] a natural tendency to disturb the total system as little as possible'. The
idea that revisions, when deliberate, tend to deploy this principle of minimal mutilation
is probably quite old and pre-dates Quine's remark.
The contemporary research in belief change is also based on implementing this


Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University


Collections: Mathematics