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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)
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