Journal of Philosophical Logic

, Volume 41, Issue 3, pp 563-593

First online:

Partially Undetermined Many-Valued Events and Their Conditional Probability

  • Franco MontagnaAffiliated withDepartment of Mathematics and Computer Science, University of Siena Email author 

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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.


Many-valued logic Conditional probability States