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Probabilistic theorem proving

Authors:

Pedro DomingosAuthors Info & Claims

Communications of the ACM, Volume 59, Issue 7

Pages 107 - 115

https://doi.org/10.1145/2936726

Published: 24 June 2016 Publication History

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Abstract

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and first-order theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving (PTP), their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how PTP can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate PTP, and show that it is superior to lifted belief propagation.

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Cited By

Krichen M(2023)Formal Methods and Validation Techniques for Ensuring Automotive Systems SecurityInformation10.3390/info1412066614:12(666)Online publication date: 18-Dec-2023
https://doi.org/10.3390/info14120666
Dilkas PBelle VMarquis PSon TKern-Isberner G(2023)Synthesising recursive functions for first-order model countingProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning10.24963/kr.2023/20(198-207)Online publication date: 2-Sep-2023
https://dl.acm.org/doi/10.24963/kr.2023/20
Dilkas P(2023)Generating Random Instances of Weighted Model CountingIntegration of Constraint Programming, Artificial Intelligence, and Operations Research10.1007/978-3-031-33271-5_26(395-416)Online publication date: 29-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-33271-5_26
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Index Terms

Probabilistic theorem proving
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Hardware
  1. Hardware validation
    1. Functional verification

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cover image Communications of the ACM

Communications of the ACM Volume 59, Issue 7

July 2016

118 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/2963119

Editor:
Moshe Y. Vardi
Association for Computing Machinery, New York, NY

Issue’s Table of Contents

Copyright © 2016 ACM.

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Publication History

Published: 24 June 2016

Published in CACM Volume 59, Issue 7

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Cited By

Krichen M(2023)Formal Methods and Validation Techniques for Ensuring Automotive Systems SecurityInformation10.3390/info1412066614:12(666)Online publication date: 18-Dec-2023
https://doi.org/10.3390/info14120666
Dilkas PBelle VMarquis PSon TKern-Isberner G(2023)Synthesising recursive functions for first-order model countingProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning10.24963/kr.2023/20(198-207)Online publication date: 2-Sep-2023
https://dl.acm.org/doi/10.24963/kr.2023/20
Dilkas P(2023)Generating Random Instances of Weighted Model CountingIntegration of Constraint Programming, Artificial Intelligence, and Operations Research10.1007/978-3-031-33271-5_26(395-416)Online publication date: 29-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-33271-5_26
Shah MSarkhel SVenugopal D(2022)Evaluating Captioning Models using Markov Logic Networks2022 IEEE International Conference on Big Data (Big Data)10.1109/BigData55660.2022.10020793(127-134)Online publication date: 17-Dec-2022
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Abboud RCeylan İDimitrov R(2022)Approximate weighted model integration on DNF structuresArtificial Intelligence10.1016/j.artint.2022.103753311(103753)Online publication date: Oct-2022
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Averkin AYarushev S(2021)Review of Research in the Field of Developing Methods to Extract Rules From Artificial Neural NetworksJournal of Computer and Systems Sciences International10.1134/S106423072106004660:6(966-980)Online publication date: 1-Nov-2021
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Dilkas PBelle V(2021)Weighted Model Counting Without Parameter VariablesTheory and Applications of Satisfiability Testing – SAT 202110.1007/978-3-030-80223-3_10(134-151)Online publication date: 2-Jul-2021
https://doi.org/10.1007/978-3-030-80223-3_10
Henderson TSimmons RSerbinowski BCline MSacharny DFan XMitiche A(2020)Probabilistic sentence satisfiability: An approach to PSATArtificial Intelligence10.1016/j.artint.2019.103199278(103199)Online publication date: Jan-2020
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Paul SKopsaftopoulos FPatterson SVarela C(2020)Dynamic Data-Driven Formal Progress Envelopes for Distributed AlgorithmsDynamic Data Driven Applications Systems10.1007/978-3-030-61725-7_29(245-252)Online publication date: 2-Oct-2020
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Gundersen O(2019)Standing on the Feet of Giants — Reproducibility in AIAI Magazine10.1609/aimag.v40i4.518540:4(9-23)Online publication date: 1-Dec-2019
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