A propositional probabilistic logic with discrete linear time for reasoning about evidence
The introduction and Section 2 of this paper are devoted to setting this paper in a wider context. To this end, the authors trace the combination of logic and probability back to Leibniz, Bernoulli, Laplace and other great historic figures. For the purposes of this paper the most relevant modern-day work is one of \textit{J. Y. Halpern} and \textit{R. Pucella} [J. Artif. Intell. Res. (JAIR) 26, 1--34 (2006; Zbl 1182.68244)] which contained an open question. This paper is aimed at answering this question.\newline In Section 3 the authors introduce a propositional logic which allows reasoning about evidence, prior and posterior probabilities, for which they define syntax and semantics. For a deducibility relation with countably many deduction steps the authors prove that the introduced logic is strongly complete.\newline The fourth section is devoted to a propositional logic for evidence and hypotheses that is enriched by two temporal operators, one operator for ``next'' and one operator for ``until''. This logic is shown to be sound and strongly complete.\newline Section 5 contains the conclusions. Here the authors explain why their completeness results required infinitary inference rules by considering the example of polynomials of odd degree over the real numbers.
scientific article; zbMATH DE number 6122045
scientific article