# zbMATH — the first resource for mathematics

A first-order conditional probability logic with iterations. (English) Zbl 1313.03008
Summary: We investigate a first-order conditional probability logic with equality, which is, up to our knowledge, the first treatise of such logic. The logic, denoted $$\mathrm{LFPOIC}^=$$, allows making statements such as: $$\mathrm{CP}_{\geq s}(\phi,\theta)$$, and $$\mathrm{CP}_{\leq s}(\phi,\theta)$$, with the intended meaning that the conditional probability of $$\phi$$ given $$\theta$$ is at least (at most) $$s$$. The corresponding syntax, semantic, and axiomatic system are introduced, and Extended completeness theorem is proven.

##### MSC:
 03B48 Probability and inductive logic 03B42 Logics of knowledge and belief (including belief change) 03B45 Modal logic (including the logic of norms)
Full Text: