Authors: Ghilezan, Silvia 
Ivetić, Jelena
Kašterović, Simona
Ognjanović, Zoran 
Savić, Nenad
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Towards Probabilistic Reasoning in Type Theory - The Intersection Type Case
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 12012 LNCS
First page: 122
Last page: 139
Conference: 11th International Symposium on Foundations of Information and Knowledge Systems, FoIKS 2020; Dortmund; Germany; 17 February 2020 through 21 February 2020
Issue Date: 1-Jan-2020
Rank: M33
ISBN: 978-3-030-39950*4
ISSN: 0302-9743
DOI: 10.1007/978-3-030-39951-1_8
The development of different probabilistic models of uncertainty has been inspired by the rapid progress in various fields, e.g. in AI, probabilistic programming, etc. Lambda calculus is a universal model of computation suitable to express programming languages concepts. Hence, different methods for probabilistic reasoning in lambda calculus have been investigated. In this paper, we develop a formal model for probabilistic reasoning about lambda terms with intersection types, which is a combination of lambda calculus and probabilistic logic. The language of lambda calculus with intersection types is endowed with a probabilistic operator. We propose a semantics based on the possible world approach. An infinitary axiomatization is given for this system and it is proved to be sound with respect to the proposed semantics.
Keywords: Intersection types | Kripke-style semantics | Lambda calculus | Probabilistic reasoning | Soundness
Publisher: Springer Link
Project: 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 
Swiss National Science Foundation, Grant 200021 165549

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