Journal of Philosophical Logic

, Volume 41, Issue 3, pp 563–593

Partially Undetermined Many-Valued Events and Their Conditional Probability


DOI: 10.1007/s10992-011-9185-3

Cite this article as:
Montagna, F. J Philos Logic (2012) 41: 563. doi:10.1007/s10992-011-9185-3


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 logicConditional probabilityStates

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of SienaSienaItaly