Partially Undetermined Many-Valued Events and Their Conditional Probability

Journal of Philosophical Logic 41 (3):563-593 (2012)
A logic for classical conditional events was investigated by Dubois and Prade. In their approach, the truth value of a conditional event may be undetermined. In this paper we extend the treatment to many-valued events. Then we support the thesis that probability over partially undetermined events is a conditional probability, and we interpret it in terms of bets in the style of de Finetti. Finally, we show that the whole investigation can be carried out in a logical and algebraic setting, and we find a logical characterization of coherence for assessments of partially undetermined events
Keywords Many-valued logic  Conditional probability  States
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DOI 10.1007/s10992-011-9185-3
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Peter Milne (1997). Bruno de Finetti and the Logic of Conditional Events. British Journal for the Philosophy of Science 48 (2):195-232.

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