A logic with conditional probability operators (Q2914029)

The authors present a sound and strongly complete infinitary axiomatization of reasoning about linear combinations of conditional probabilities. The logical language is rich enough to formalize sentences of the form: The conditional probability of \(\alpha\) given \(\beta\) (in the opinion of Agent 1) is at least the sum of the conditional probabilities of \(\alpha\) given \(\gamma\) (in the opinion of Agent 2) and two times the conditional probabilities of \(\gamma\) given \(\delta\) (in the opinion of Agent 3). Decidability of the logic is proven. The corresponding decision procedure is in PSPACE (in the case of only one agent).