Abductive Reasoning with Probabilistic Commonsense

Joseph Cotnareanu, Chiara Roverato, Han Zhou, Didier Chételat, Yingxue Zhang, Mark Coates
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:21584-21595, 2026.

Abstract

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals’ distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-cotnareanu26a, title = {Abductive Reasoning with Probabilistic Commonsense}, author = {Cotnareanu, Joseph and Roverato, Chiara and Zhou, Han and Ch\'{e}telat, Didier and Zhang, Yingxue and Coates, Mark}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {21584--21595}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/cotnareanu26a/cotnareanu26a.pdf}, url = {https://proceedings.mlr.press/v306/cotnareanu26a.html}, abstract = {Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals’ distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.} }
Endnote
%0 Conference Paper %T Abductive Reasoning with Probabilistic Commonsense %A Joseph Cotnareanu %A Chiara Roverato %A Han Zhou %A Didier Chételat %A Yingxue Zhang %A Mark Coates %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-cotnareanu26a %I PMLR %P 21584--21595 %U https://proceedings.mlr.press/v306/cotnareanu26a.html %V 306 %X Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals’ distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.
APA
Cotnareanu, J., Roverato, C., Zhou, H., Chételat, D., Zhang, Y. & Coates, M.. (2026). Abductive Reasoning with Probabilistic Commonsense. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:21584-21595 Available from https://proceedings.mlr.press/v306/cotnareanu26a.html.

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