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Non-standard probability, coherence and conditional probability on many-valued events. (English) Zbl 1316.03009
Summary: The usual coherence criterion by de Finetti is extended both to many-valued events and to conditional probability. Special attention is paid to assessments in which the betting odds for conditioning events are zero. This case is treated by means of infinitesimal probabilities. We propose a rationality criterion, called stable coherence, which is stronger than coherence in the sense of no sure loss.

MSC:
03B48 Probability and inductive logic
03B50 Many-valued logic
06D35 MV-algebras
28E05 Nonstandard measure theory
91B16 Utility theory
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