Abductive Reasoning with Probabilistic Commonsense

Joseph Cotnareanu, Chiara Roverato, Han Zhou, Didier Chételat, Yingxue Zhang, Mark Coates

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.

Lay Summary:

This work studies a key limitation of neurosymbolic reasoning systems: commonsense assumptions are not universally shared across people. Existing approaches typically treat commonsense as deterministic, but in reality, many “obvious” assumptions are subjective or uncertain.

To address this, we introduce PACS (Probabilistic Abductive Common Sense), a framework that models commonsense reasoning probabilistically by sampling diverse assumptions using large language models (LLMs) and formal solvers, then aggregating conclusions across belief distributions.

We also introduce a probabilistic approach to chain-of-thought generation. Rather than sampling reasoning traces uniformly, we derive a principled objective that samples chains according to their expected reasoning efficiency by minimizing the expected number of inference steps required to reach a solution. This connects probabilistic inference, search efficiency, and reasoning diversity within a unified framework.

Across multiple benchmarks, PACS outperforms chain-of-thought prompting, prior neurosymbolic methods, and search-based approaches.

Link To Code: https://github.com/networkslab/PACS

Primary Area: Optimization->Discrete and Combinatorial Optimization

Keywords: Logical Reasoning, Comonsense Reasoning, Abductive Reasoning, Logic, Search

Submission Number: 27212