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A logic with conditional probability operators. (English) Zbl 1265.03010

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).

MSC:

03B48 Probability and inductive logic
03B25 Decidability of theories and sets of sentences
03B42 Logics of knowledge and belief (including belief change)
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