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.
Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views of the reasoning process. Our hypothesis is that this logical subspace captures logical reasoning capabilities in LLMs that are shared across views while remaining independent of surface forms. To verify this, we employ Canonical Correlation Analysis on the paired residual activations from natural-language and symbolic-language reasoning chains, learning a low-dimensional subspace with maximum cross-view correlation. Furthermore, we design a training-free approach that steers LLMs reasoning chain along this logical subspace, thereby leveraging the complementary reasoning signals from both views. Experiments on four logical reasoning benchmarks demonstrate the effectiveness of our approach, improving accuracy by up to 11 percentage points and generalizing well on out-of-domain problems.
Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate unchecked through inference chains. We present a symbolic reasoning scaffold that operationalizes Peirce's tripartite inference -- abduction, deduction, and induction -- as an explicit protocol for LLM-assisted reasoning. The framework enforces logical consistency through five algebraic invariants (the Gamma Quintet), the strongest of which -- the Weakest Link bound -- ensures that no conclusion in a reasoning chain can exceed the reliability of its least-supported premise. This principle, independently grounded as weakest link resolution in possibilistic logic and empirically validated for chain-of-thought reasoning, prevents logical inconsistencies from accumulating across multi-step inference. We verify all invariants through a property-based testing suite of 100 properties and 16 fuzz tests over 10^5+ generated cases, providing a verified reference implementation of the invariants suitable as a foundation for future reasoning benchmarks.
As large language models (LLMs) continue to advance in complex reasoning tasks, they have learned to heavily prioritize explicit conditions provided in the input. However, in everyday commonsense reasoning, this mechanism exposes a critical vulnerability which we term Salience Bias: models become easily hijacked by useless explicit distractors (e.g., numerical values), leading them to ignore the implicit physical or commonsense prerequisites of a task. A critical open question is whether this failure reflects a genuine gap in commonsense knowledge or merely its suppression under misleading task framing. To investigate this, we construct the SaliTrap Benchmark, a high-quality dataset across four trap dimensions. Evaluating 12 state-of-the-art LLMs, we find that all mainstream models suffer significantly from salience bias, with severity scaling with distractor density and detecting the trap often decoupled from actually avoiding it. Crucially, by re-eliciting the same models with the task framing stripped away, we show that this is overwhelmingly a failure of \textbf{knowledge suppression rather than knowledge absence}: a context-free knowledge probe alone recovers over 90% of sycophantic-compliance failures, revealing that the requisite commonsense is intrinsically present but actively crowded out by salient distractors that lure the model into over-compliant, unnecessary computation. Building on this diagnosis, we further show that lightweight, inference-time prompting alone substantially closes the gap without any retraining. Our findings relocate the bottleneck of commonsense reasoning failures from model competence to elicitation, and we release SaliTrap as a testbed for this blind spot. The codes are available at https://github.com/Wuzheng02/SaliTrap.