Authors: Ghilezan, Silvia 
Ivetić, Jelena
Kašterović, Simona
Ognjanović, Zoran 
Savić, Nenad
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
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
Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security 
Representations of logical structures and formal languages and their application in computing 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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