4,447 research outputs found
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
Games for the Strategic Influence of Expectations
We introduce a new class of games where each player's aim is to randomise her
strategic choices in order to affect the other players' expectations aside from
her own. The way each player intends to exert this influence is expressed
through a Boolean combination of polynomial equalities and inequalities with
rational coefficients. We offer a logical representation of these games as well
as a computational study of the existence of equilibria.Comment: In Proceedings SR 2014, arXiv:1404.041
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