|Title:||Probabilistic reasoning about simply typed lambda terms||Journal:||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)||Volume:||10703 LNCS||First page:||170||Last page:||189||Conference:||International Symposium on Logical Foundations of Computer Science, LFCS 2018; FL; United States; 8 January 2018 through 11 January 2018||Issue Date:||1-Jan-2018||Rank:||M33||ISBN:||978-3-319-72055-5||ISSN:||0302-9743||DOI:||10.1007/978-3-319-72056-2_11||Abstract:||
Reasoning with uncertainty has gained an important role in computer science, artificial intelligence and cognitive science. These applications urge for development of formal models which capture reasoning of probabilistic features. We propose a formal model for reasoning about probabilities of simply typed lambda terms. We present its syntax, Kripke-style semantics and axiomatic system. The main results are the corresponding soundness and strong completeness, which rely on two key facts: the completeness of simple type assignment and the existence of a maximal consistent extension of a consistent set.
|Keywords:||Probabilistic logic | Simply typed lambda calculus | Soundness | Strong completeness||Publisher:||Springer Link||Project:||Schweizerischer Nationalfonds zur förderung der Wissenschaftlichen Forschung
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