When Decodability Is Not Enough: Logical Validity Representations, Behavioral Dissociation, and Causal Tests in Language Models

Large language models can look capable of logical reasoning, but correct or incorrect answers alone tell us little about what the model represents internally. We study logical verification in five open-weight transformer models using matched valid--invalid premise--claim pairs that vary across inference families, semantic domains, templates, and difficulty levels. Despite near-chance behavioral performance, logical validity is often almost perfectly decodable from hidden states and remains strongly decodable under held-out templates, domains, and inference families. Validity also remains highly decodable on behaviorally incorrect examples in the conditions where correctness-conditioned evaluation is well defined. At the same time, exhaustive leave-one-out tests reveal clear limits to this generalization, and interventions along probe-derived validity directions have only weak, nonspecific effects compared with random controls. Our results suggest that representing validity, expressing it in behavior, and using it causally are distinct. Validity related information can be strongly decodable from a model's hidden states without being reliably expressed in its output.

Evaluating the Semantic Specificity of Representation Steering in Language Models

Localized Representation Steering (LRS) is widely used to correct reasoning pathologies in large language models. However, standard benchmark evaluations can easily be fooled by superficial label overrides, creating a false impression of reasoning circuit repairs. In this work, we propose Cross-Rule Transfer (CRT), a diagnostic framework that audits representational interventions by evaluating them on rule families where the model is natively competent. Evaluating late-layer LRS for a widespread logical failure, contradiction blindness, reveals that the intervention merely injects a global label bias: applying the steering vector to rules the model already handles correctly (99.6% baseline) degrades performance to 40.4% by forcing false contradiction predictions. We support this diagnosis with four complementary controls (direct logit bias equivalence, control vector label-flipping, cross-model grafting, and early-layer steering checks), providing a rigorous methodology to distinguish genuine reasoning repairs from superficial label overrides.

From Atomic Evidence to Logical Composition: Structured Compositional Reasoning over Compound Answer Options

Large language models often fail when answer options require combining atomic judgments under explicit logical operators, even when they judge the individual atoms correctly. We study compound options connected by AND, OR, and NEITHER/NOR, introducing a framework that decomposes each option into atomic answers and scores contrastive hypotheses about each one, so the model never sees a compound option. An operator-constrained integer linear program then composes the calibrated scores into a single prediction. We evaluate on LOGICAL-COMMONSENSEQA and introduce LOGICAL-SATA, a reading-comprehension benchmark derived from SATA-Bench. Our framework improves Macro-F1 from 48.3 to 77.0 on the human-validated LOGICAL-COMMONSENSEQA split and from 47.0 to 75.6 on LOGICAL-SATA, with the largest gains on NEITHER/NOR.

Think Deep, Speak Once: Relit, A Recursive Latent Implicit Transformer Framework

Chain-of-Thought (CoT) prompting has become the dominant paradigm for eliciting reasoning in Large Language Models (LLMs), yet it creates substantial computational overhead by forcing models to externalize intermediate reasoning steps as discrete tokens. Recent latent reasoning approaches attempt to internalize this process within continuous hidden states. One of the latest advancements in the field of latent reasoning, Tiny Recursive Models (TRMs) excel at symbolic reasoning but struggle to preserve semantic coherence in natural language settings. To bridge this gap, we introduce ReLIT (Recursive Latent Implicit Transformer), a hybrid framework that grounds deep recursive reasoning within the rich semantic representations of a foundational model. ReLIT augments a frozen LLM backbone (TinyLlama-1.1B) with a lightweight, trainable recursive block that iteratively refines its latent thinking (z) before committing to a final output, structurally solving linguistic intuition from algorithmic processing and enabling "deep thinking" via gradient-isolated recurrent loops without the latency of explicit token generation. Empirically, ReLIT achieves high parameter efficiency on the GLoRE logical reasoning benchmark, matching or outperforming significantly larger models on challenging tasks such as ProofWriter and RuleTaker despite minimal supervision. These results demonstrate that reasoning capability can be scaled efficiently through recurrent depth rather than parameter width, offering a principled framework for semantically grounded implicit reasoning.

Benchmarking LLM Competence on Logical Inference over Probability Operators

Both expressions of uncertainty and inferences are ubiquitous in natural language, and valid inferences over natural-language expressions of uncertainty are necessary for not only everyday conversations but also for high-stakes domains such as medicine and law. While large language models are increasingly evaluated on logical reasoning tasks, disentangling principled, symbolic reasoning from clever surface-level pattern matching is fraught with difficulty. We introduce a benchmark for reasoning over probability operators--inference over sentences with gradable epistemic modals (e.g., probably, might, must) containing 14,320 procedurally-generated English prompts across fifteen inference templates, systematically varying question form, negation strategy, and surface content. Evaluating 29 models, we find that most show answer biases independent of the logical form, a systematic preference for Yes or No. We summarize this with a competence floor: the worse of a model's accuracy on Yes-correct and No-correct items. Only 9 of 29 models exceed random chance. We also test variations in question form, verb phrases/activity, and both the gender and origin of names used in the prompts, finding biases across every axis.

Logical Judgments Under Pressure: Diagnosing Syllogistic Stability with Learned Soft Prefixes

To test how correct logical judgments respond to learned context, we prepend a soft prefix to an exactly labeled syllogistic reasoning benchmark while keeping the model fixed. Soft prefixes are opaque continuous vectors, so we characterize them through the behavior they induce across controlled variations in logical form and interface. By studying which prefixes succeed and how their effects generalize, we characterize how learned contextual pressure can override correct judgments and expose limits in a model's logical stability. Across Qwen3.6-35B-A3B MoE, Qwen3-8B, and Gemma 4 31B, learned prefixes redirect many correct answers and remain effective across unseen forms and interface changes. In repeated tests with Qwen3.6 MoE and Gemma, they outperform paired random controls in all 16 model--direction--split comparisons by 37 to 99 percentage points. Qwen3.6 MoE flip rates remain between 72% and 90% across wording and prompt changes, while Gemma validity prefixes retain 54% to 56% flip compared with less than 1% for matched random prefixes. Diagnostic tests show that the dominant effect is a broad preference for one answer meaning rather than fixed-symbol forcing or a logical operation that transfers reliably between tasks. The form of this bias differs across models. In both Qwen models, simple score models often predict which judgments will flip but not how far their margins will move, whereas Gemma's overall response is more closely approximated by the same models. These results show that the dominant behavioral effect of successful soft prefixes is a broad answer preference, while the remaining response reveals substantial model-specific differences in logical stability.

Neurosymbolics for Data Engineering: Achieving Long Context Token Reduction Without Finetuning

Large Language Models are increasingly deployed for sophisticated data engineering tasks such as generating structured queries from natural language, Text-to-SQL, and automating complex spreadsheet operations. However, maximizing their utility demands both higher finetuning-free accuracy and solutions to the computational bottleneck imposed by the Transformer architectures inherent quadratic (On2) time complexity. This paper introduces a novel drop-in neurosymbolic layer designed to seamlessly integrate into existing LLM backbones enhancing logical reasoning and mitigating long-context resource consumption. On the reasoning front, the layer immediately and significantly improves performance yielding an average accuracy increase of 85% across rigorous benchmarks including BIRD-CRITIC and LiveSQLBench, critically achieving these gains without any task specific finetuning or RLHF. Concurrently, we repurpose this approach to address the severe computational strain of long context inference. By leveraging symbolic processing to prioritize and compress relevant contextual information the layer reduces the effective token usage by over 50% and brings the effective time complexity down from O(n2) to approximately O(n) on certain long context tasks. This dual impact approach not only makes LLMs substantially more reliable for data engineering but also drastically reduces the computational pressure on inference chips, making long context tasks more manageable and cost effective.

Beyond Logical Forms: LLM-Extracted Patterns for Fallacy Classification

In today's fast-paced information era, logical fallacies, defined as defective patterns of reasoning, inevitably contribute to the growth of information disorder. However, often fallacies appear in nuanced forms that complicate automated classification. In this study, we investigate whether merging abstract logical structures with context-level linguistic cues proves beneficial for fallacy classification, developing a framework that inductively extracts such patterns from fallacious examples and their explanations using Large Language Models (LLMs). We evaluate the impact of these patterns across different LLMs and experimental zero- and one-shot configurations, showing statistically significant improvements over zero-shot baselines and outperforming competing approaches. Cross-dataset experiments validate generalization, establishing data-driven pattern extraction as an effective method for generating logical representations.

Coherence Under Commitment: Probing Generalization and Vacuous Memorization in LLM Logical Reasoning

Large language models (LLMs) deployed for logical reasoning in knowledge-intensive domains exhibit a subtle but critical failure: coherence can be vacuously achieved through systematic abstention. A model that withholds commitment to either entailment or refutation satisfies negation consistency while providing no utility. We introduce Coherence Under Commitment (CUC), a dual-query evaluation paradigm that jointly measures consistency and decisiveness. CUC contributes three innovations: (1) a commitment score $c(\varphi) = p(\varphi) + p(\lnot\varphi)$ quantifying probability mass allocated to decisive outcomes; (2) a \textbf{deterministic elicitation protocol} via normalized YES/NO log probabilities, eliminating sampling variance; and (3) a 3-way decision framework (True/False/Uncertain) operationalizing the coherence-commitment trade-off into metrics. Experiments on four open-weight LLMs (1B-3B) across 204 FOLIO examples expose a sharp frontier. Qwen2.5-3B achieves near-zero contradiction ($\mathbb{E}[v_{\mathrm{neg}}]{=}0.025$) but only $7.4\%$ coverage, while TinyLlama-1.1B reaches $79.4\%$ coverage with violations on every example. Coherence-only evaluation would rank the abstaining model first; CUC exposes this as vacuous, and the frontier generalizes to LogiQA~v2 ($ρ{=}0.97$). We argue that evaluation must report both coherence and non-vacuous commitment and release a toolkit for standardized assessment.

ChLogic: Evaluating Robustness of Logical Reasoning in Chinese Expressions

Large language models perform increasingly well on standardized logical reasoning benchmarks, but whether this ability remains robust beyond English is unclear. We introduce ChLogic, an English--Chinese aligned benchmark that tests whether models preserve logical reasoning performance when the same latent logical structure is expressed in English and diverse Chinese surface realizations. Built from formal logical templates, the benchmark contains three data sets: (i) the General aligned set, derived from 60 General Propositions across nine template families; (ii) the Difficult aligned set, derived from 40 Difficult Problems; and (iii) the Chinese-only set, covering 15 language-specific phenomenon types. Each aligned item pairs one English reference expression with five Chinese realizations. Experiments on Qwen3, Ministral, and GLM models reveal a persistent English--Chinese performance gap. Back-translation from standard Chinese into English often improves performance on the General aligned set, but produces mixed effects on the Difficult aligned set, where Qwen3-32B and GLM-5.1 perform worse after translation. These results indicate that Chinese surface realization, translation artifacts, and model-specific behavior jointly affect multilingual logical reasoning. Overall, ChLogic provides a useful stress test for the robustness of multilingual reasoning.

Benchmarking Knowledge Editing using Logical Rules

Large Language Models (LLMs) are increasingly deployed in real-world applications that require access to up-to-date knowledge. However, retraining LLMs is computationally expensive. Therefore, knowledge editing techniques are crucial for maintaining current information and correcting erroneous assertions within pre-trained models. Current benchmarks for knowledge editing primarily focus on recalling edited facts, often neglecting their logical consequences. To address this limitation, we introduce a new benchmark designed to evaluate how knowledge editing methods handle the logical consequences of a single fact edit. Our benchmark extracts relevant logical rules from a knowledge graph for a given edit. Then, it generates multi-hop questions based on these rules to assess the impact on logical consequences. Our findings indicate that while existing knowledge editing approaches can accurately insert direct assertions into LLMs, they frequently fail to inject entailed knowledge. Specifically, experiments with popular methods like ROME and FT reveal a substantial performance gap, up to 24%, between evaluations on directly edited knowledge and on entailed knowledge. This highlights the critical need for semantics-aware evaluation frameworks in knowledge editing.

More Yap Less Meaning: Uncovering Self-Improvement Behavior in SLMs

Recently, language models have made rapid progress across various domains and applications. However, their capability for self-improvement, i.e., whether they are adept at recognising and correcting flaws in their own reasoning, remains dubious. In this study, we address this question by constructing a sufficiency test to rigorously examine the self-correction capabilities of small language models (SLMs). We propose a minimal three-step self-correction pipeline that collects initial SLM answers, prompts the same model to generate hints for its incorrect responses given the ground truth, and feeds the model the same question with its own feedback to refine the initial answer. We evaluate a variety of instruction-tuned and reasoning SLMs in this experimental setup on arithmetic and logical reasoning benchmarks. Our findings show that SLMs with injected hint sentences yield only a 4.4 percent gain over initial question-answering accuracy. Even though the correct answer was provided alongside the model's incorrect reasoning, the evaluated SLMs fail to understand what was missing in their reasoning and show minimal semantic difference between hints that lead to corrections and ones that do not. Furthermore, our experiments show that longer hints are positively correlated with incorrect final answers, suggesting that longer deliberation on problems can hinder the reasoning process, meaning that SLMs do not necessarily scale in performance with a larger compute budget.