A Representation Result for Value-based Contraction

Sven-Ove Hansson and Erik Olsson studied in Hansson and Olsson (Notre Dame Journal of Formal Logic, 36(1), 103–119 1995) the logical properties of an operation of contraction first proposed by Isaac Levi in Levi (1991). 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.

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