The mean value of a fuzzy number
Fuzzy Sets and Systems - Fuzzy Numbers
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
An introduction to possibilistic and fuzzy logics
Readings in uncertain reasoning
A Logic for Reasoning about Upper Probabilities
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Reasoning about Uncertainty
A probabilistic logic based on the acceptability of gambles
International Journal of Approximate Reasoning
Characterizing and reasoning about probabilistic and non-probabilistic expectation
Journal of the ACM (JACM)
Shallow Models for Non-iterative Modal Logics
KI '08 Proceedings of the 31st annual German conference on Advances in Artificial Intelligence
A logic for reasoning about upper probabilities
Journal of Artificial Intelligence Research
Reasoning about hybrid probabilistic knowledge bases
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
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Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the underlying representation of uncertainty. We give sound and complete axiomatizations for the logic in the case that the underlying representation is (a) probability, (b) sets of probability measures, (c) belief functions, and (d) possibility measures. We show that this logic is more expressive than the corresponding logic for reasoning about likelihood in the case of sets of probability measures, but equi-expressive in the case of probability, belief, and possibility. Finally, we show that satisfiability for these logics is NP-complete, no harder than satisfiability for propositional logic.