Probability theory and causation: A branching space-times analysis

Abstract
We provide a formally rigorous framework for integrating singular causation, as understood by Nuel Belnap's theory of causae causantes, and objective single case probabilities. The central notion is that of a causal probability space whose sample space consists of causal alternatives. Such a probability space is generally not isomorphic to a product space. We give a causally motivated statement of the Markov condition and an analysis of the concept of screening-off. Causal dependencies and probabilities 1.1 Background: causation in branching space-times 1.2 What are probabilities defined for? Basic transitions 2.1 Basics of basic transitions 2.2 Sets of basic transitions Causal probability theory 3.1 Some simple cases 3.2 General causal probabilities 3.3 Application: probability of suprema of a chain.
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DOI 10.1093/bjps/axi132
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Leszek Wroński & Tomasz Placek (2009). On Minkowskian Branching Structures☆. Studies in History and Philosophy of Science Part B 40 (3):251-258.
Jeremy Butterfield (2007). Stochastic Einstein Locality Revisited. British Journal for the Philosophy of Science 58 (4):805 - 867.

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