Theory of linear and integer programming
Theory of linear and integer programming
Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
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
Randomized algorithms
Reasoning about Uncertainty
Great expectations: part II: Generalized expected utility as a universal decision rule
Artificial Intelligence
A logic for reasoning about upper probabilities
Journal of Artificial Intelligence Research
Great expectations: part I: on the customizability of generalized expected utility
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in 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.