Weighted Model Counting With Function Symbols

Vaishak Belle
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:848-857, 2017.

Abstract

Probabilistic relational languages lift the syntax of relational logic for the specification of large-scale probabilistic graphical models, often admitting con- cise descriptions for interacting random variables over classes, hierarchies and constraints. The emer- gence of weighted model counting as an effective and general approach to probabilistic inference has further allowed practitioners to reason about hetero- geneous representations, such as Markov logic net- works and ProbLog programs, by encoding them as a logical theory. However, much of this work has been limited to an essentially propositional setting: the logical model is understood in terms of ground formulas over a fixed and finite domain; no infinite domains, and certainly no function symbols (other than constants). On the one hand, this is not sur- prising, because such features are very problematic from a decidability viewpoint, but on the other, they turn out to be very attractive from the point of view of machine learning applications when there is un- certainty about the existence and identity of objects. In this paper, we reconsider the problem of proba- bilistic reasoning in a logical language with function symbols, and establish some key results that permit effective algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-belle17a, title = {Weighted Model Counting With Function Symbols}, author = {Belle, Vaishak}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {848--857}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/belle17a/belle17a.pdf}, url = {https://proceedings.mlr.press/r15/belle17a.html}, abstract = {Probabilistic relational languages lift the syntax of relational logic for the specification of large-scale probabilistic graphical models, often admitting con- cise descriptions for interacting random variables over classes, hierarchies and constraints. The emer- gence of weighted model counting as an effective and general approach to probabilistic inference has further allowed practitioners to reason about hetero- geneous representations, such as Markov logic net- works and ProbLog programs, by encoding them as a logical theory. However, much of this work has been limited to an essentially propositional setting: the logical model is understood in terms of ground formulas over a fixed and finite domain; no infinite domains, and certainly no function symbols (other than constants). On the one hand, this is not sur- prising, because such features are very problematic from a decidability viewpoint, but on the other, they turn out to be very attractive from the point of view of machine learning applications when there is un- certainty about the existence and identity of objects. In this paper, we reconsider the problem of proba- bilistic reasoning in a logical language with function symbols, and establish some key results that permit effective algorithms.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Weighted Model Counting With Function Symbols %A Vaishak Belle %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-belle17a %I PMLR %P 848--857 %U https://proceedings.mlr.press/r15/belle17a.html %V R15 %X Probabilistic relational languages lift the syntax of relational logic for the specification of large-scale probabilistic graphical models, often admitting con- cise descriptions for interacting random variables over classes, hierarchies and constraints. The emer- gence of weighted model counting as an effective and general approach to probabilistic inference has further allowed practitioners to reason about hetero- geneous representations, such as Markov logic net- works and ProbLog programs, by encoding them as a logical theory. However, much of this work has been limited to an essentially propositional setting: the logical model is understood in terms of ground formulas over a fixed and finite domain; no infinite domains, and certainly no function symbols (other than constants). On the one hand, this is not sur- prising, because such features are very problematic from a decidability viewpoint, but on the other, they turn out to be very attractive from the point of view of machine learning applications when there is un- certainty about the existence and identity of objects. In this paper, we reconsider the problem of proba- bilistic reasoning in a logical language with function symbols, and establish some key results that permit effective algorithms. %Z Reissued by PMLR on 04 October 2026.
APA
Belle, V.. (2017). Weighted Model Counting With Function Symbols. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:848-857 Available from https://proceedings.mlr.press/r15/belle17a.html. Reissued by PMLR on 04 October 2026.

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