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Exhaustive Classication of Finite Classical Probability Spaces with Regard to the Notion of Causal Up-to-n-closedness

Marczyk, Michal and Wronski, Leszek (2009) Exhaustive Classication of Finite Classical Probability Spaces with Regard to the Notion of Causal Up-to-n-closedness. [Preprint]

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Abstract

Extending the ideas from (Hofer-Szabó and Rédei [2006]), we introduce the notion of causal up-to-n-closedness of probability spaces. A probability space is said to be causally up-to-n-closed with respect to a relation of independence R_ind iff for any pair of correlated events belonging to R_ind the space provides a common cause or a common cause system of size at most n. We prove that a finite classical probability space is causally up-to-3-closed w.r.t. the relation of logical independence iff its probability measure is constant on the set of atoms of non-0 probability. (The latter condition is a weakening of the notion of measure uniformity.) Other independence relations are also considered.


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Item Type: Preprint
Creators:
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Marczyk, Michal
Wronski, Leszek
Keywords: common cause; common cause systems; common cause closedness
Subjects: General Issues > Causation
Depositing User: Leszek Wronski
Date Deposited: 17 Jun 2009
Last Modified: 07 Oct 2010 15:18
Item ID: 4714
URI: http://philsci-archive.pitt.edu/id/eprint/4714

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