Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond

Vaishak Belle

doi:10.5281/zenodo.8121236

Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract / Description of output

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 that does 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 ran- dom variables, both discrete and continuous distributions, as well as programming languages built on top of such features to include recursion and branching control.

Original language	English
Title of host publication	Logics in Artificial Intelligence
Subtitle of host publication	18th European Conference, JELIA 2023, Dresden, Germany, September 20–22, 2023, Proceedings
Publisher	Springer
Pages	35-46
Number of pages	12
ISBN (Electronic)	9783031436192
ISBN (Print)	9783031436185
DOIs	https://doi.org/10.5281/zenodo.8121236 https://doi.org/10.1007/978-3-031-43619-2_3
Publication status	Published - 24 Sept 2023
Event	18th Edition of the European Conference on Logics in Artificial Intelligence - Dresden, Germany Duration: 20 Sept 2023 → 22 Sept 2023 https://jelia2023.inf.tu-dresden.de/

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th Edition of the European Conference on Logics in Artificial Intelligence
Abbreviated title	JELIA 2023
Country/Territory	Germany
City	Dresden
Period	20/09/23 → 22/09/23
Internet address	https://jelia2023.inf.tu-dresden.de/

Keywords / Materials (for Non-textual outputs)

first-order logic
probabilistic logic
programs

Access to Document

10.5281/zenodo.8121236Licence: Creative Commons: Attribution (CC-BY)
10.1007/978-3-031-43619-2_3Licence: All Rights Reserved

Excursions in first-order_BELLE_DOA10072023_AFV_CC BYAccepted author manuscript, 113 KBLicence: Creative Commons: Attribution (CC-BY)

https://link.springer.com/chapter/10.1007/978-3-031-43619-2_3Licence: All Rights Reserved

UKRI Trustworthy Autonomous Systems Node in Governance and Regulation
Ramamoorthy, R., Belle, V., Bundy, A., Jackson, P., Lascarides, A. & Rajan, A.
EPSRC
1/11/20 → 30/04/24
Project: Research
Efficient Inference and Learning in Probabilistic Logical Models
Belle, V.
Other (Learned Society)
1/10/19 → 30/09/24
Project: Research

18th Edition of the European Conference on Logics in Artificial Intelligence
Vaishak Belle (Keynote/plenary speaker)
21 Sept 2023
Activity: Participating in or organising an event types › Participation in conference

Cite this

Belle, V. (2023). Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond. In Logics in Artificial Intelligence: 18th European Conference, JELIA 2023, Dresden, Germany, September 20–22, 2023, Proceedings (pp. 35-46). (Lecture Notes in Computer Science). Springer. https://doi.org/10.5281/zenodo.8121236, https://doi.org/10.1007/978-3-031-43619-2_3

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title = "Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond",

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 that does 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 ran- dom variables, both discrete and continuous distributions, as well as programming languages built on top of such features to include recursion and branching control.",

keywords = "first-order logic, probabilistic logic, programs",

author = "Vaishak Belle",

note = "Funding Information: 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). Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.; 18th Edition of the European Conference on Logics in Artificial Intelligence, JELIA 2023 ; Conference date: 20-09-2023 Through 22-09-2023",

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doi = "10.5281/zenodo.8121236",

language = "English",

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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 Logics in Artificial Intelligence: 18th European Conference, JELIA 2023, Dresden, Germany, September 20–22, 2023, Proceedings. Lecture Notes in Computer Science, Springer, pp. 35-46, 18th Edition of the European Conference on Logics in Artificial Intelligence, Dresden, Saxony, Germany, 20/09/23. https://doi.org/10.5281/zenodo.8121236, https://doi.org/10.1007/978-3-031-43619-2_3

Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond. / Belle, Vaishak.
Logics in Artificial Intelligence: 18th European Conference, JELIA 2023, Dresden, Germany, September 20–22, 2023, Proceedings. Springer, 2023. p. 35-46 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond

AU - Belle, Vaishak

N1 - Funding Information: 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). Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

PY - 2023/9/24

Y1 - 2023/9/24

N2 - 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 that does 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 ran- dom variables, both discrete and continuous distributions, as well as programming languages built on top of such features to include recursion and branching control.

AB - 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 that does 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 ran- dom variables, both discrete and continuous distributions, as well as programming languages built on top of such features to include recursion and branching control.

KW - first-order logic

KW - probabilistic logic

KW - programs

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DO - 10.5281/zenodo.8121236

M3 - Conference contribution

SN - 9783031436185

T3 - Lecture Notes in Computer Science

SP - 35

EP - 46

BT - Logics in Artificial Intelligence

PB - Springer

T2 - 18th Edition of the European Conference on Logics in Artificial Intelligence

Y2 - 20 September 2023 through 22 September 2023

ER -

Belle V. Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond. In Logics in Artificial Intelligence: 18th European Conference, JELIA 2023, Dresden, Germany, September 20–22, 2023, Proceedings. Springer. 2023. p. 35-46. (Lecture Notes in Computer Science). doi: 10.5281/zenodo.8121236, 10.1007/978-3-031-43619-2_3

Excursions in first-order logic and probability: infinitely many random variables, continuous distributions, recursive programs and beyond

Abstract / Description of output

Publication series

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Projects

UKRI Trustworthy Autonomous Systems Node in Governance and Regulation

Efficient Inference and Learning in Probabilistic Logical Models

Activities

18th Edition of the European Conference on Logics in Artificial Intelligence

Cite this