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International Symposium on Foundations of Information and Knowledge Systems

FoIKS 2020: Foundations of Information and Knowledge Systems pp 122–139Cite as

Towards Probabilistic Reasoning in Type Theory - The Intersection Type Case

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12012))

Abstract

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.

This work was supported by the Serbian Ministry of Education and Science through projects ON174026, III 044006 and by the Swiss National Science Foundation grant 200021\(\_\)165549.

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Notes

  1. 1.

    For any real number \(\epsilon > 0\) there exists an \(n \in \mathbb {N}\) such that \(\frac{1}{n} < \epsilon \).

  2. 2.

    Note that the notion of a consistent set is different than usual. We have one additional condition, namely condition (2).

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Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Trg Dositeja Obradovića 6, 21000, Novi Sad, Serbia

    Silvia Ghilezan, Jelena Ivetić & Simona Kašterović

  2. Mathematical Institute SANU, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Silvia Ghilezan & Zoran Ognjanović

  3. Institute of Computer Science, University of Bern, Neubrueckstrasse 10, 3012, Bern, Switzerland

    Nenad Savić

Authors
  1. Silvia Ghilezan
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  2. Jelena Ivetić
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  3. Simona Kašterović
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  4. Zoran Ognjanović
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  5. Nenad Savić
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Corresponding author

Correspondence to Simona Kašterović .

Editor information

Editors and Affiliations

  1. CNRS, University of Toulouse, Toulouse, France

    Andreas Herzig

  2. University of Helsinki, Helsinki, Finland

    Juha Kontinen

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Ghilezan, S., Ivetić, J., Kašterović, S., Ognjanović, Z., Savić, N. (2020). Towards Probabilistic Reasoning in Type Theory - The Intersection Type Case. In: Herzig, A., Kontinen, J. (eds) Foundations of Information and Knowledge Systems. FoIKS 2020. Lecture Notes in Computer Science(), vol 12012. Springer, Cham. https://doi.org/10.1007/978-3-030-39951-1_8

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  • DOI: https://doi.org/10.1007/978-3-030-39951-1_8

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