De Finetti theorem and Borel states in [0,1]-valued algebraic logic
International Journal of Approximate Reasoning
The coherence of Łukasiewicz assessments is NP-complete
International Journal of Approximate Reasoning
On varieties of MV-algebras with internal states
International Journal of Approximate Reasoning
A logical characterization of coherence for imprecise probabilities
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
A Notion of Coherence for Books on Conditional Events in Many-valued Logic
Journal of Logic and Computation
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
States in Łukasiewicz logic correspond to probabilities of rational polyhedra
International Journal of Approximate Reasoning
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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.