Contraction: On the decision-theoretical origins of minimal change and entrenchment

Synthese 152 (1):129 - 154 (2006)
  We present a decision-theoretically motivated notion of contraction which, we claim, encodes the principles of minimal change and entrenchment. Contraction is seen as an operation whose goal is to minimize loses of informational value. The operation is also compatible with the principle that in contracting A one should preserve the sentences better entrenched than A (when the belief set contains A). Even when the principle of minimal change and the latter motivation for entrenchment figure prominently among the basic intuitions in the works of, among others, Quine and Ullian (1978), Levi (1980, 1991), Harman (1988) and Gärdenfors (1988), formal accounts of belief change (AGM, KM – see Gärdenfors (1988); Katsuno and Mendelzon (1991)) have abandoned both principles (see Rott (2000)). We argue for the principles and we show how to construct a contraction operation, which obeys both. An axiom system is proposed. We also prove that the decision-theoretic notion of contraction can be completely characterized in terms of the given axioms. Proving this type of completeness result is a well-known open problem in the field, whose solution requires employing both decision-theoretical techniques and logical methods recently used in belief change
Keywords belief revision  contraction  decision theory  entrenchment  withdrawal
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DOI 10.1007/s11229-005-0351-4
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References found in this work BETA
Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.

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Citations of this work BETA
AGM 25 Years.Eduardo Fermé & Sven Ove Hansson - 2011 - Journal of Philosophical Logic 40 (2):295-331.
AGM 25 Years: Twenty-Five Years of Research in Belief Change.Eduardo Fermé & Sven Ove Hansson - 2011 - Journal of Philosophical Logic 40 (2):295 - 331.
A Representation Result for Value-Based Contraction.Horacio Arló Costa & Hailin Liu - forthcoming - Journal of Philosophical Logic:1-25.

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