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Excursions in First-Order Logic and Probability: Infinitely Many Random Variables, Continuous Distributions, Recursive Programs and Beyond

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

The unification of the first-order logic and probability has been seen as a long-standing concern in philosophy, AI and mathematics. In this talk, I will briefly review our recent results on revisiting that unification. Although there are plenty of approaches in communities such as statistical relational learning, automated planning, and neuro-symbolic AI that leverage and develop languages with logical and probabilistic aspects, they almost always restrict the representation as well as the semantic framework in various ways which do not fully explain how to combine first-order logic and probability theory in a general way. In many cases, this restriction is justified because it may be necessary to focus on practicality and efficiency. However, the search for a restriction-free mathematical theory remains ongoing. In this article, we discuss our recent results regarding the development of languages that support arbitrary quantification, possibly infinitely many random variables, both discrete and continuous distributions, as well as programming languages built on top of such features to include recursion and branching control.

This material introduces the topic of my keynote at the 18th Edition of the European Conference on Logics in Artificial Intelligence (JELIA), September 20–22, 2023. This research was partly supported by a Royal Society University Research Fellowship, UK, and partly supported by a grant from the UKRI Strategic Priorities Fund, UK to the UKRI Research Node on Trustworthy Autonomous Systems Governance and Regulation (EP/V026607/1, 2020–2024).

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Authors and Affiliations

  1. University of Edinburgh, Edinburgh, UK

    Vaishak Belle

  2. Alan Turing Institute, London, UK

    Vaishak Belle

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  1. Vaishak Belle
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Correspondence to Vaishak Belle .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Belle, V. (2023). Excursions in First-Order Logic and Probability: Infinitely Many Random Variables, Continuous Distributions, Recursive Programs and Beyond. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_3

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_3

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