Inferring Latent Intentions: Attributional Natural Language Inference in LLM Agents

Attributional inference, the ability to predict latent intentions behind observed actions, is a critical yet underexplored capability for large language models (LLMs) operating in multi-agent environments. Traditional natural language inference (NLI), in fact, fails to capture the nuanced, intention-driven reasoning essential for complex interactive systems. To address this gap, we introduce Attributional NLI (Att-NLI), a framework that extends NLI with principles from social psychology to assess an agent's capacity for abductive intentional inference (generating hypotheses about latent intentions), and subsequent deductive verification (drawing valid logical conclusions). We instantiate Att-NLI via a textual game, Undercover-V, experimenting with three types of LLM agents with varying reasoning capabilities and access to external tools: a standard NLI agent using only deductive inference, an Att-NLI agent employing abductive-deductive inference, and a neuro-symbolic Att-NLI agent performing abductive-deductive inference with external theorem provers. Extensive experiments demonstrate a clear hierarchy of attributional inference capabilities, with neuro-symbolic agents consistently outperforming others, achieving an average win rate of 17.08%. Our results underscore the role that Att-NLI can play in developing agents with sophisticated reasoning capabilities, highlighting, at the same time, the potential impact of neuro-symbolic AI in building rational LLM agents acting in multi-agent environments.

Logic-Parametric Neuro-Symbolic NLI: Controlling Logical Formalisms for Verifiable LLM Reasoning

Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and adaptability. We propose a logic-parametric framework for neuro-symbolic NLI that treats the underlying logic not as a static background, but as a controllable component. Using the LogiKEy methodology, we embed a range of classical and non-classical formalisms into higher-order logic (HOL), enabling a systematic comparison of inference quality, explanation refinement, and proof behavior. We focus on normative reasoning, where the choice of logic has significant implications. In particular, we compare logic-external approaches, where normative requirements are encoded via axioms, with logic-internal approaches, where normative patterns emerge from the logic's built-in structure. Extensive experiments demonstrate that logic-internal strategies can consistently improve performance and produce more efficient hybrid proofs for NLI. In addition, we show that the effectiveness of a logic is domain-dependent, with first-order logic favouring commonsense reasoning, while deontic and modal logics excel in ethical domains. Our results highlight the value of making logic a first-class, parametric element in neuro-symbolic architectures for more robust, modular, and adaptable reasoning.

Learning to Disentangle Latent Reasoning Rules with Language VAEs: A Systematic Study

Incorporating explicit reasoning rules within the latent space of language models (LMs) offers a promising pathway to enhance generalisation, interpretability, and controllability. While current Transformer-based language models have shown strong performance on Natural Language Inference (NLI) tasks, they often rely on memorisation rather than rule-based inference. This work investigates how reasoning rules can be explicitly embedded and memorised within the LMs through Language Variational Autoencoders (VAEs). We propose a complete pipeline for learning reasoning rules within Transformer-based language VAEs. This pipeline encompasses three rule-based reasoning tasks, a supporting theoretical framework, and a practical end-to-end architecture. The experiment illustrates the following findings: Disentangled reasoning: Under explicit signal supervision, reasoning rules - viewed as functional mappings - can be disentangled within the encoder's parametric space. This separation results in distinct clustering of rules in the output feature space. Prior knowledge injection: injecting reasoning information into the Query enables the model to more effectively retrieve the stored value Value from memory based on Key. This approach offers a simple method for integrating prior knowledge into decoder-only language models. Performance bottleneck: In mathematical reasoning tasks using Qwen2.5(0.5B), increasing sample count doesn't improve performance beyond a point. Moreover, ffn layers are better than attention layers at preserving the separation of reasoning rules in the model's parameters.

Beyond Gold Standards: Epistemic Ensemble of LLM Judges for Formal Mathematical Reasoning

Autoformalization plays a crucial role in formal mathematical reasoning by enabling the automatic translation of natural language statements into formal languages. While recent advances using large language models (LLMs) have shown promising results, methods for automatically evaluating autoformalization remain underexplored. As one moves to more complex domains (e.g., advanced mathematics), human evaluation requires significant time and domain expertise, especially as the complexity of the underlying statements and background knowledge increases. LLM-as-a-judge presents a promising approach for automating such evaluation. However, existing methods typically employ coarse-grained and generic evaluation criteria, which limit their effectiveness for advanced formal mathematical reasoning, where quality hinges on nuanced, multi-granular dimensions. In this work, we take a step toward addressing this gap by introducing a systematic, automatic method to evaluate autoformalization tasks. The proposed method is based on an epistemically and formally grounded ensemble (EFG) of LLM judges, defined on criteria encompassing logical preservation (LP), mathematical consistency (MC), formal validity (FV), and formal quality (FQ), resulting in a transparent assessment that accounts for different contributing factors. We validate the proposed framework to serve as a proxy for autoformalization assessment within the domain of formal mathematics. Overall, our experiments demonstrate that the EFG ensemble of LLM judges is a suitable emerging proxy for evaluation, more strongly correlating with human assessments than a coarse-grained model, especially when assessing formal qualities. These findings suggest that LLM-as-judges, especially when guided by a well-defined set of atomic properties, could offer a scalable, interpretable, and reliable support for evaluating formal mathematical reasoning.

Faithful and Robust LLM-Driven Theorem Proving for NLI Explanations

Natural language explanations play a fundamental role in Natural Language Inference (NLI) by revealing how premises logically entail hypotheses. Recent work has shown that the interaction of large language models (LLMs) with theorem provers (TPs) can help verify and improve the validity of NLI explanations. However, TPs require translating natural language into machine-verifiable formal representations, a process that introduces the risk of semantic information loss and unfaithful interpretation, an issue compounded by LLMs' challenges in capturing critical logical structures with sufficient precision. Moreover, LLMs are still limited in their capacity for rigorous and robust proof construction within formal verification frameworks. To mitigate issues related to faithfulness and robustness, this paper investigates strategies to (1) alleviate semantic loss during autoformalisation, (2) efficiently identify and correct syntactic errors in logical representations, (3) explicitly use logical expressions to guide LLMs in generating structured proof sketches, and (4) increase LLMs' capacity of interpreting TP's feedback for iterative refinement. Our empirical results on e-SNLI, QASC and WorldTree using different LLMs demonstrate that the proposed strategies yield significant improvements in autoformalisation (+18.46%, +34.2%, +39.77%) and explanation refinement (+29.5%, +51.5%, +41.25%) over the state-of-the-art model. Moreover, we show that specific interventions on the hybrid LLM-TP architecture can substantially improve efficiency, drastically reducing the number of iterations required for successful verification.

Enhancing Logical Reasoning in Language Models via Symbolically-Guided Monte Carlo Process Supervision

Large language models (LLMs) have shown promising performance in mathematical and logical reasoning benchmarks. However, recent studies have pointed to memorization, rather than generalization, as one of the leading causes for such performance. LLMs, in fact, are susceptible to content variations, demonstrating a lack of robust symbolic abstractions supporting their reasoning process. To improve reliability, many attempts have been made to combine LLMs with symbolic methods. Nevertheless, existing approaches fail to effectively leverage symbolic representations due to the challenges involved in developing reliable and scalable verification mechanisms. In this paper, we propose to overcome such limitations by generating symbolic reasoning trajectories and select the high-quality ones using a process reward model automatically tuned based on Monte Carlo estimation. The trajectories are then employed via fine-tuning methods to improve logical reasoning and generalization. Our results on logical reasoning benchmarks such as FOLIO and LogicAsker show the effectiveness of the proposed method with large gains on frontier and open-weight models. Moreover, additional experiments on claim verification reveal that fine-tuning on the generated symbolic reasoning trajectories enhances out-of-domain generalizability, suggesting the potential impact of symbolically-guided process supervision in alleviating the effect of memorization on LLM reasoning.

Mitigating Content Effects on Reasoning in Language Models through Fine-Grained Activation Steering

Large language models (LLMs) frequently demonstrate reasoning limitations, often conflating content plausibility (i.e., material inference) with logical validity (i.e., formal inference). This can result in biased inferences, where plausible arguments are incorrectly deemed logically valid or vice versa. Mitigating this limitation is critical, as it undermines the trustworthiness and generalizability of LLMs in applications that demand rigorous logical consistency. This paper investigates the problem of mitigating content biases on formal reasoning through activation steering. Specifically, we curate a controlled syllogistic reasoning dataset to disentangle formal validity from content plausibility. After localising the layers responsible for formal and material inference, we investigate contrastive activation steering methods for test-time interventions. An extensive empirical analysis on different LLMs reveals that contrastive steering consistently supports linear control over content biases. However, we observe that a static approach is insufficient for improving all the tested models. We then leverage the possibility to control content effects by dynamically determining the value of the steering parameters via fine-grained conditional methods. We found that conditional steering is effective on unresponsive models, achieving up to 15% absolute improvement in formal reasoning accuracy with a newly introduced kNN-based method (K-CAST). Finally, additional experiments reveal that steering for content effects is robust to prompt variations, incurs minimal side effects on language modeling capabilities, and can partially generalize to out-of-distribution reasoning tasks. Practically, this paper demonstrates that activation-level interventions can offer a scalable strategy for enhancing the robustness of LLMs, contributing towards more systematic and unbiased formal reasoning.

PEIRCE: Unifying Material and Formal Reasoning via LLM-Driven Neuro-Symbolic Refinement

A persistent challenge in AI is the effective integration of material and formal inference - the former concerning the plausibility and contextual relevance of arguments, while the latter focusing on their logical and structural validity. Large Language Models (LLMs), by virtue of their extensive pre-training on large textual corpora, exhibit strong capabilities in material inference. However, their reasoning often lacks formal rigour and verifiability. At the same time, LLMs' linguistic competence positions them as a promising bridge between natural and formal languages, opening up new opportunities for combining these two modes of reasoning. In this paper, we introduce PEIRCE, a neuro-symbolic framework designed to unify material and formal inference through an iterative conjecture-criticism process. Within this framework, LLMs play the central role of generating candidate solutions in natural and formal languages, which are then evaluated and refined via interaction with external critique models. These critiques include symbolic provers, which assess formal validity, as well as soft evaluators that measure the quality of the generated arguments along linguistic and epistemic dimensions such as plausibility, coherence, and parsimony. While PEIRCE is a general-purpose framework, we demonstrate its capabilities in the domain of natural language explanation generation - a setting that inherently demands both material adequacy and formal correctness.

Improving Chain-of-Thought Reasoning via Quasi-Symbolic Abstractions

Chain-of-Though (CoT) represents a common strategy for reasoning in Large Language Models (LLMs) by decomposing complex tasks into intermediate inference steps. However, explanations generated via CoT are susceptible to content biases that negatively affect their robustness and faithfulness. To mitigate existing limitations, recent work has proposed using logical formalisms coupled with external symbolic solvers. However, fully symbolic approaches possess the bottleneck of requiring a complete translation from natural language to formal languages, a process that affects efficiency and flexibility. To achieve a trade-off, this paper investigates methods to disentangle content from logical reasoning without a complete formalisation. In particular, we present QuaSAR (for Quasi-Symbolic Abstract Reasoning), a variation of CoT that guides LLMs to operate at a higher level of abstraction via quasi-symbolic explanations. Our framework leverages the capability of LLMs to formalise only relevant variables and predicates, enabling the coexistence of symbolic elements with natural language. We show the impact of QuaSAR for in-context learning and for constructing demonstrations to improve the reasoning capabilities of smaller models. Our experiments show that quasi-symbolic abstractions can improve CoT-based methods by up to 8% accuracy, enhancing robustness and consistency on challenging adversarial variations on both natural language (i.e. MMLU-Redux) and symbolic reasoning tasks (i.e., GSM-Symbolic).

Formalizing Complex Mathematical Statements with LLMs: A Study on Mathematical Definitions

Thanks to their linguistic capabilities, LLMs offer an opportunity to bridge the gap between informal mathematics and formal languages through autoformalization. However, it is still unclear how well LLMs generalize to sophisticated and naturally occurring mathematical statements. To address this gap, we investigate the task of autoformalizing real-world mathematical definitions -- a critical component of mathematical discourse. Specifically, we introduce two novel resources for autoformalisation, collecting definitions from Wikipedia (Def_Wiki) and arXiv papers (Def_ArXiv). We then systematically evaluate a range of LLMs, analyzing their ability to formalize definitions into Isabelle/HOL. Furthermore, we investigate strategies to enhance LLMs' performance including refinement through external feedback from Proof Assistants, and formal definition grounding, where we guide LLMs through relevant contextual elements from formal mathematical libraries. Our findings reveal that definitions present a greater challenge compared to existing benchmarks, such as miniF2F. In particular, we found that LLMs still struggle with self-correction, and aligning with relevant mathematical libraries. At the same time, structured refinement methods and definition grounding strategies yield notable improvements of up to 16% on self-correction capabilities and 43% on the reduction of undefined errors, highlighting promising directions for enhancing LLM-based autoformalization in real-world scenarios.