The Measurement of Ranks and the Laws of Iterated Contraction

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Artificial Intelligence 172 (10):1195-1218 (2008)
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Abstract

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.

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10.1016/j.artint.2008.03.002

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Wolfgang Spohn
Universität Konstanz

Citations of this work

Degrees of belief.Franz Huber & Christoph Schmidt-Petri (eds.) - 2009 - London: Springer.
Belief and Degrees of Belief.Franz Huber - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer.
A Ranking‐Theoretic Approach to Conditionals.Wolfgang Spohn - 2013 - Cognitive Science 37 (6):1074-1106.

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References found in this work

On the logic of iterated belief revision.Adnan Darwiche & Judea Pearl - 1997 - Artificial Intelligence 89 (1-2):1-29.
Iterated revision and minimal change of conditional beliefs.Craig Boutilier - 1996 - Journal of Philosophical Logic 25 (3):263 - 305.
Reversing the Levi identity.Sven Ove Hansson - 1993 - Journal of Philosophical Logic 22 (6):637 - 669.

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