Multiple contraction revisited

Multiple contraction consists in giving up several beliefs at once. The treatments of multiple contraction in AGM belief revision theory have remained unsatisfactory. The paper proposes a clear, plausible, and general model for multiple contraction in ranking-theoretic terms according to which multiple contraction turns out to reduce to single contractions. The belief set multiply contracted by {A 1, …, A n } is just the intersection of all the belief sets singly contracted by A i (i = 1, …, n).

[1]  André Fuhrmann.  An Essay on Contraction , 1996 .

[2]  Sven Ove Hansson,et al.  A textbook of belief dynamics - theory change and database updating , 1999, Applied logic series.

[3]  Peter Gärdenfors,et al.  Knowledge in Flux , 1988 .

[4]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[5]  Wolfgang Spohn,et al.  Eine Theorie der Kausalität , 1983 .

[6]  Peter Gärdenfors,et al.  Knowledge in Flux: Modeling the Dynamics of Epistemic States , 2008 .

[7]  Wolfgang Spohn,et al.  Ordinal Conditional Functions: A Dynamic Theory of Epistemic States , 1988 .

[8]  Jacek Malinowski,et al.  Towards Mathematical Philosophy , 2009, Trends in logic.

[9]  Hans Rott,et al.  Change, choice and inference - a study of belief revision and nonmonotonic reasoning , 2001, Oxford logic guides.

[10]  André Fuhrmann,et al.  Relevant logics, modal logics and theory change , 1988 .

[11]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[12]  SVEN OVE HANSSON,et al.  Reversing the Levi identity , 1993, J. Philos. Log..

[13]  Hans Rott,et al.  Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators , 2009, Towards Mathematical Philosophy.

[14]  André Fuhrmann,et al.  A survey of multiple contractions , 1994, J. Log. Lang. Inf..

[15]  Wolfgang Spohn.  A Survey of Ranking Theory , 2009 .

[16]  William Harper,et al.  Causation in decision, belief change, and statistics , 1988 .

[17]  I. Levi.  Mild Contraction: Evaluating Loss of Information Due to Loss of Belief , 2004 .

[18]  Wolfgang Spohn,et al.  The measurement of ranks and the laws of iterated contraction , 2008, Artif. Intell..

[19]  Sven Ove Hansson,et al.  A Textbook Of Belief Dynamics , 1999 .

[20]  F. Huber,et al.  Degrees of Belief , 2009 .