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

Logics for Non-Cooperative Games with Expectations

International audienceWe introduce the logics E(G) for reasoning about probabilistic expectation over classes G of games with discrete polynomial payoff functions represented by finite-valued Lukasiewicz formulas and provide completeness and complexity results. In addition, we introduce a new class of games where players’ expected payoff functions are encoded by E(G)-formulas. In these games each player’s aim is to randomise her strategic choices in order to affect the other players’ expectations over an outcome as well as their own. We offer a logical and computational characterisation of this new class of games

Logics for Non-Cooperative Games with Expectations

We introduce the logics E(G) for reasoning about probabilistic expectation over classes G of games with discrete polynomial payoff functions represented by finite-valued Lukasiewicz formulas and provide completeness and complexity results. In addition, we introduce a new class of games where players' expected payoff functions are encoded by E(G)-formulas. In these games each player's aim is to randomise her strategic choices in order to affect the other players' expectations over an outcome as well as their own. We offer a logical and computational characterisation of this new class of games.Godo acknowledges support from the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER CSD 2007-0022). Marchioni acknowledges support from the Marie Curie Project NAAMSI (FP7-PEOPLE-2011-IEF).Peer Reviewe

Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation

1. INTRODUCTION One of the most important notions in probability theory is that of expectation.The expected value of a random variable is, in a sense, the single number tha