Partially Undetermined Many-Valued Events and Their Conditional Probability

Journal of Philosophical Logic 41 (3):563-593 (2012)
Abstract
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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Protoalgebraic Logics.Janusz Czelakowski - 2001 - Kluwer Academic Publishers.
Weakly Implicative (Fuzzy) Logics I: Basic Properties. [REVIEW]Petr Cintula - 2006 - Archive for Mathematical Logic 45 (6):673-704.
Nelson Algebras Through Heyting Ones: I.Andrzej Sendlewski - 1990 - Studia Logica 49 (1):105-126.

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