| Authors: | Savić, Nenad Doder, Dragan Ognjanović, Zoran |
Title: | A first-order logic for reasoning about higher-order upper and lower probabilities | Journal: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Volume: | 10369 LNAI | First page: | 491 | Last page: | 500 | Conference: | 14th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2017; Lugano; Switzerland; 10 July 2017 through 14 July 2017 | Issue Date: | 1-Jan-2017 | Rank: | M33 | ISBN: | 978-3-319-61581-3 | ISSN: | 0302-9743 | DOI: | 10.1007/978-3-319-61581-3_44 | Abstract: | We present a first-order probabilistic logic for reasoning about the uncertainty of events modeled by sets of probability measures. In our language, we have formulas that essentially say that “according to agent Ag, for all x, formula α(x) holds with the lower probability at least 1/3 ”. Also, the language is powerful enough to allow reasoning about higher order upper and lower probabilities. We provide corresponding Kripke-style semantics, axiomatize the logic and prove that the axiomatization is sound and strongly complete (every satisfiable set of formulas is consistent). |
Keywords: | Axiomatization | Probabilistic logic | Strong completeness | Uncertainty | Publisher: | Springer Link |
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