6 research outputs found
A logic for reasoning about upper probabilities
We present a propositional logic %which can be used to reason about the
uncertainty of events, where the uncertainty is modeled by a set of probability
measures assigning an interval of probability to each event. We give a sound
and complete axiomatization for the logic, and show that the satisfiability
problem is NP-complete, no harder than satisfiability for propositional logic.Comment: A preliminary version of this paper appeared in Proc. of the 17th
Conference on Uncertainty in AI, 200
Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation
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.Comment: To appear in Journal of the AC