Regular Article: Tensor Products and the Loomis驴Sikorski Theorem for MV-Algebras
Advances in Applied Mathematics
Reasoning about Uncertainty
Belief models: An order-theoretic investigation
Annals of Mathematics and Artificial Intelligence
A probabilistic logic based on the acceptability of gambles
International Journal of Approximate Reasoning
Notes on conditional previsions
International Journal of Approximate Reasoning
De Finetti theorem and Borel states in [0,1]-valued algebraic logic
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
MV-algebras with internal states and probabilistic fuzzy logics
International Journal of Approximate Reasoning
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
Non-reversible betting games on fuzzy events: Complexity and algebra
Fuzzy Sets and Systems
Non-standard probability, coherence and conditional probability on many-valued events
International Journal of Approximate Reasoning
Jon Williamson: In Defence of Objective Bayesianism
Minds and Machines
Hi-index | 0.08 |
Whilst supported by compelling arguments, the representation of uncertainty by means of (subjective) probability does not enjoy a unanimous consensus. A substantial part of the relevant criticisms point to its alleged inadequacy for representing ignorance as opposed to uncertainty. The purpose of this paper is to show how a strong justification for taking belief as probability, namely the Dutch Book argument, can be extended naturally so as to provide a logical characterization of coherence for imprecise probability, a framework which is widely believed to accommodate some fundamental features of reasoning under ignorance. The appropriate logic for our purposes is an algebraizable logic whose equivalent algebraic semantics is a variety of MV-algebras with an additional internal unary operation representing upper probability (these algebras will be called UMV-algebras).