Neuro-Symbolic Reasoning

Recent large language models (LLMs) have achieved impressive reasoning milestones but continue to struggle with high computational costs, logical inconsistencies, and sharp performance degradation on high-complexity problems. While neuro-symbolic methods attempt to mitigate these issues by coupling LLMs with symbolic reasoners, existing approaches typically rely on monotonic logics (e.g., SMT) that cannot represent defeasible reasoning -- essential components of human cognition. We present "LLM+ASP," a framework that translates natural language into Answer Set Programming (ASP), a nonmonotonic formalism based on stable model semantics. Unlike prior "LLM+ASP" approaches that require manually authored knowledge modules, domain-specific prompts, or evaluation restricted to single problem classes, our framework operates without any per-task engineering and applies uniformly across diverse reasoning tasks. Our system utilizes an automated self-correction loop where structured feedback from the ASP solver enables iterative refinement. Evaluating across six diverse benchmarks, we demonstrate that: (1) stable model semantics allow LLMs to naturally express default rules and exceptions, outperforming SMT-based alternatives by significant margins on nonmonotonic tasks; (2) iterative self-correction is the primary driver of performance, effectively replacing the need for handcrafted domain knowledge; (3) compact in-context reference guides substantially outperform verbose documentation, revealing a "context rot" phenomenon where excessive context hinders constraint adherence.

Deploying a neuro-symbolic task planner on a new domain today requires significant manual effort: a domain expert must author relaxation and complementary rules, and hundreds of training problems must be solved to supervise a Graph Neural Network (GNN) object scorer. We propose LLM-Flax, a three-stage framework that eliminates all three sources of manual effort using a locally hosted LLM given only a PDDL domain file. Stage 1 automatically generates relaxation and complementary rules via structured prompting with format validation and self-correction. Stage 2 introduces LLM-guided failure recovery with a feasibility-gated budget policy that explicitly reserves API latency cost before each LLM call, preventing the downstream relaxation fallback from being starved. Stage 3 replaces the domain-trained GNN entirely with zero-shot LLM object importance scoring, requiring no training data. We evaluate all three stages on the MazeNamo benchmark across 10x10, 12x12, and 15x15 grids (8 benchmarks total). LLM-Flax achieves average SR 0.945 versus the manual baseline's 0.828 (+0.117), matching or outperforming manual rules on every one of the eight benchmarks. On 12x12 Expert, LLM-Flax attains SR 0.733 where the manual planner fails entirely (SR 0.000); on 15x15 Hard, it achieves SR 1.000 versus Manual's 0.900. Stage 3 demonstrates feasibility (SR 0.720 on 12x12 Hard with no training data) but faces a context-window bottleneck at scale, pointing to the primary open challenge for future work.

Compositional generalization remains a foundational weakness of modern neural networks, limiting their robustness and applicability in domains requiring out-of-distribution reasoning. A central, yet unverified, assumption in neuro-symbolic AI is that compositional reasoning will emerge as a byproduct of successful symbol grounding. This work presents the first systematic empirical analysis to challenge this assumption by disentangling the contributions of grounding and reasoning. To operationalize this investigation, we introduce the Iterative Logic Tensor Network ($i$LTN), a fully differentiable architecture designed for multi-step deduction. Using a formal taxonomy of generalization -- probing for novel entities, unseen relations, and complex rule compositions -- we demonstrate that a model trained solely on a grounding objective fails to generalize. In contrast, our full $i$LTN, trained jointly on perceptual grounding and multi-step reasoning, achieves high zero-shot accuracy across all tasks. Our findings provide conclusive evidence that symbol grounding, while necessary, is insufficient for generalization, establishing that reasoning is not an emergent property but a distinct capability that requires an explicit learning objective.

Background & Objectives: In the last decade, Machine learning research has grown rapidly, but large models are reaching their soft limits demonstrating diminishing returns and still lack solid reasoning abilities. These limits could be surpassed through synergistic combination of Machine Learning scalability and rigid reasoning. Methods: In this work, we propose a theoretical framework for reasoning through object-relations in an automated manner integrated with Artificial Neural Networks. We present a formal analysis of the Reasoning, and we show the theory in practice through a paradigm integrating Reasoning and Machine Learning. Results: This paradigm is a system that solves Intelligence Quotient problems without any prior knowledge of the problem. Our system achieves 98.03% solving rate corresponding to the top 1% percentile or 132-144 iq score. This result is only limited by the small size of the model and the processing capabilities of the machine it run on. Conclusions: With the integration of prior knowledge in the system and the expansion of the dataset, the system can be generalized to solve a large category of problems. The functionality of the system inherently favors the solution of such problems in few-shot or zero-shot attempts.

ULLER (Unified Language for LEarning and Reasoning) offers a unified first-order logic (FOL) syntax, enabling its knowledge bases to be used directly across a wide range of neurosymbolic systems. The original specification endows this syntax with three pairwise independent semantics: classical, fuzzy, and probabilistic, each accompanied by dedicated semantic rules. We show that these seemingly disparate semantics are all instances of one categorical framework based on monads, the very construct that models side effects in functional programming. This enables the modular addition of new semantics and systematic translations between them. As example, we outline the addition of generalised quantification in Logic Tensor Networks (LTN) to arbitrary (also infinite) domains by extending the Giry monad to probability spaces. In particular, our approach allows a modular implementation of ULLER in Python and Haskell, of which we have published initial versions on GitHub.

There are 7,407 languages in the world. But, what about the languages that are not there in the world? Are humans so narrow minded that we don't care about the languages aliens communicate in? Aliens are humans too! In the 2016 movie Arrival, Amy Adams plays a linguist, Dr. Louise Banks who, by learning to think in an alien language (Heptapod) formed of non-sequential sentences, gains the ability to transcend time and look into the future. In this work, I aim to explore the representation and reasoning of vision-language concepts in a neuro-symbolic language, and study improvement in analytical reasoning abilities and efficiency of "thinking systems". With Qwen3-VL-2B-Instruct as base model and 4 $\times$ Nvidia H200 GPU nodes, I achieve an accuracy improvement of 3.33% on a vision-language evaluation dataset consisting of math, science, and general knowledge questions, while reducing the reasoning tokens by 75% over SymPy. I've documented the compute challenges faced, scaling possibilities, and the future work to improve thinking in a neuro-symbolic language in vision-language models. The training and inference setup can be found here: https://github.com/i-like-bfs-and-dfs/wolfram-reasoning.

Robotic systems operating in human environments must reason about how object interactions evolve over time, which actions are currently being performed, and what manipulation step is likely to follow. Classical enriched Semantic Event Chains (eSECs) provide an interpretable relational description of manipulation, but remain primarily descriptive and do not directly support uncertainty-aware decision making. In this paper, we propose eSEC-LAM, a neuro-symbolic framework that transforms eSECs into an explicit event-level symbolic state for manipulation understanding. The proposed formulation augments classical eSECs with confidence-aware predicates, functional object roles, affordance priors, primitive-level abstraction, and saliency-guided explanation cues. These enriched symbolic states are derived from a foundation-model-based perception front-end through deterministic predicate extraction, while current-action inference and next-primitive prediction are performed using lightweight symbolic reasoning over primitive pre- and post-conditions. We evaluate the proposed framework on EPIC-KITCHENS-100, EPIC-KITCHENS VISOR, and Assembly101 across action recognition, next-primitive prediction, robustness to perception noise, and explanation consistency. Experimental results show that eSEC-LAM achieves competitive action recognition, substantially improves next-primitive prediction, remains more robust under degraded perceptual conditions than both classical symbolic and end-to-end video baselines, and provides temporally consistent explanation traces grounded in explicit relational evidence. These findings demonstrate that enriched Semantic Event Chains can serve not only as interpretable descriptors of manipulation, but also as effective internal states for neuro-symbolic action reasoning.

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.

Modern artificial intelligence remains fundamentally divided between the continuous, probabilistic spaces of Foundation Models and the discrete, deterministic structures of Knowledge Graphs. While Retrieval-Augmented Generation (RAG) attempts to connect them by serializing graph data into text, we argue this lexical bridging is merely a superficial patch. In this paper, we formalize the underlying structural and geometric friction as the Impedance Mismatch. By categorizing current neuro-symbolic integration strategies into a three-tiered hierarchy, we demonstrate that neither surface-level prompt injection nor continuous representation alignment can preserve the strict logical motifs required for reliable multi-hop reasoning. We define the specific mathematical limits, such as the Lexical Bottleneck and Topological Collapse, that show current architectures will eventually hallucinate or conflate semantic nodes. To achieve true semantic fusion, we propose a rigorous theoretical roadmap. We advocate for natively internalizing discrete symbolic structures through Structured Residual Streams, utilizing Vector Symbolic Architectures for latent sub-graph injection, and performing model updates via Orthogonal Subspace Editing. This actionable framework paves the way for models that seamlessly fuse the precision of symbolic logic with the expressivity of parametric memory.

More than half of the global population struggles to meet their civil justice needs due to limited legal resources. While Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, significant challenges remain even at the foundational step of legal issue identification. To investigate LLMs' capabilities in this task, we constructed a dataset from 769 real-world Malaysian Contract Act court cases, using GPT-4o to extract facts and generate candidate legal issues, annotated by senior legal experts, which reveals a critical limitation: while LLMs generate diverse issue candidates, their precision remains inadequate (GPT-4o achieves only 62%). To address this gap, we propose LePREC (Legal Professional-inspired Reasoning Elicitation and Classification), a neuro-symbolic framework combining neural generation with structured statistical reasoning. LePREC consists of: (1) a neuro component leverages LLMs to transform legal descriptions into question-answer pairs representing diverse analytical factors, and (2) a symbolic component applies sparse linear models over these discrete features, learning explicit algebraic weights that identify the most informative reasoning factors. Unlike end-to-end neural approaches, LePREC achieves interpretability through transparent feature weighting while maintaining data efficiency through correlation-based statistical classification. Experiments show a 30-40% improvement over advanced LLM baselines, including GPT-4o and Claude, confirming that correlation-based factor-issue analysis offers a more data-efficient solution for relevance decisions.

Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training paradigms to optimize end-to-end Large Language Models (LLMs), they typically treat formal code as flat sequences, neglecting the hierarchical logic inherent in mathematical statements. In this work, we introduce Decompose, Structure, and Repair (DSR), a neuro-symbolic framework that restructures autoformalization into a modular pipeline. DSR decomposes statements into logical components and maps them to structured operator trees, leveraging this topological blueprint to precisely localize and repair errors via sub-tree refinement. Furthermore, we introduce PRIME, a benchmark of 156 undergraduate and graduate-level theorems selected from canonical textbooks and expertly annotated in Lean 4. Experimental results demonstrate that DSR establishes a new state-of-the-art, consistently outperforming baselines under equivalent computational budgets. The datasets, model, and code are available at https://github.com/XiaoyangLiu-sjtu/DSR.

Large language models (LLMs) are highly capable at language generation, but they remain unreliable when reasoning requires explicit symbolic structure, multi-step inference, and interpretable uncertainty. This paper presents a neuro-symbolic framework for translating natural-language reasoning problems into executable formal representations using first-order logic (FOL) and Narsese, the language of the Non-Axiomatic Reasoning System (NARS). To support this direction, we introduce NARS-Reasoning-v0.1, a benchmark of natural-language reasoning problems paired with FOL forms, executable Narsese programs, and three gold labels: True, False, and Uncertain. We develop a deterministic compilation pipeline from FOL to executable Narsese and validate retained examples through runtime execution in OpenNARS for Applications (ONA), ensuring that the symbolic targets are not only syntactically well formed but also behaviorally aligned with the intended answer. We further present Language-Structured Perception (LSP), a formulation in which an LLM is trained to produce reasoning-relevant symbolic structure rather than only a final verbal response. As an initial proof of concept, we also train and release a Phi-2 LoRA adapter on NARS-Reasoning-v0.1 for three-label reasoning classification, showing that the benchmark can support supervised adaptation in addition to executable evaluation. Overall, the paper positions executable symbolic generation and execution-based validation as a practical path toward more reliable neuro-symbolic reasoning systems.

We present FregeLogic, a hybrid neuro-symbolic system for SemEval-2026 Task 11 (Subtask 1), which addresses syllogistic validity prediction while reducing content effects on predictions. Our approach combines an ensemble of five LLM classifiers, spanning three open-weights models (Llama 4 Maverick, Llama 4 Scout, and Qwen3-32B) paired with varied prompting strategies, with a Z3 SMT solver that serves as a formal logic tiebreaker. The central hypothesis is that LLM disagreement within the ensemble signals likely content-biased errors, where real-world believability interferes with logical judgment. By deferring to Z3's structurally-grounded formal verification on these disputed cases, our system achieves 94.3% accuracy with a content effect of 2.85 and a combined score of 41.88 in nested 5-fold cross-validation on the dataset (N=960). This represents a 2.76-point improvement in combined score over the pure ensemble (39.12), with a 0.9% accuracy gain, driven by a 16% reduction in content effect (3.39 to 2.85). Adopting structured-output API calls for Z3 extraction reduced failure rates from ~22% to near zero, and an Aristotelian encoding with existence axioms was validated against task annotations. Our results suggest that targeted neuro-symbolic integration, applying formal methods precisely where ensemble consensus is lowest, can improve the combined accuracy-plus-content-effect metric used by this task.

Human-centred systems require an understanding of human actions in the physical world. Temporally extended sequences of actions are intentional and structured, yet existing methods for recognising what actions are performed often do not attempt to capture their structure, particularly how the actions are executed. This, however, is crucial for assessing the quality of the action's execution and its differences from other actions. To capture the internal mechanics of actions, we introduce a domain-specific language EXACT that represents human motions as underspecified motion programs, interpreted as reward-generating functions for zero-shot policy inference using forward-backwards representations. By leveraging the compositional nature of EXACT motion programs, we combine individual policies into an executable neuro-symbolic model that uses program structure for compositional modelling. We evaluate the utility of the proposed pipeline for creating executable action models by analysing motion-capture data to understand human actions, for the tasks of human action segmentation and action anomaly detection. Our results show that the use of executable action models improves data efficiency and captures intuitive relationships between actions compared with monolithic, task-specific approaches.

AlphaGeometry represents a milestone in neuro-symbolic reasoning, yet its architecture faces a log-linear scaling bottleneck within its symbolic deduction engine that limits its efficiency as problem complexity increases. Recent technical reports suggest that current domain-specific languages may be isomorphic as input representations to natural language, interchanging them acts as a performance-invariant transformation, implying that current neural guidance relies on superficial encodings rather than structural understanding. This paper addresses this representation bottleneck by proposing a logic-to-topology encoding designed to reveal the structural invariants of a model's latent space under a transformation of its input space. By leveraging the Logic of Observation, we utilize the duality between provability in observable theories and topologies to propose a logic-to-topology encoder for the input space. We introduce the concept of the "topological dual of a dataset", a transformation that bridges formal logic, topology, and neural processing. This framework serves as a Rosetta Stone for neuro-symbolic AI, providing a principled pathway for the mechanistic interpretability of how models navigate complex discovery paths.

Do Theory of Mind (ToM) benchmarks really test theory of mind, or are they actually testing parsing and algorithmic state tracking? While benchmarks vary modality and dialogue length, this paper finds that they re-encode the same few state transition algorithms. We create PDDL-Mind, a neuro-symbolic approach that recovers such algorithms and upstream inductive biases of ToM benchmarks explicitly by parsing narratives into the Planning Domain Definition Language (PDDL) and executes candidate actions against a predefined set of update algorithms. Doing so provides program-verified state traces to the model. We use our method's performance gain to audit how much of a benchmark's difficulty our inductive bias absorbs. Across MMToM, MuMA, and FanToM, outsourcing parsing to programs alone brings performance close to strong agentic pipelines, while outsourcing state tracking to PDDL moves GPT-4o to close-to-human performance. We demonstrate that complex ToM benchmarks primarily punishes Large Language Models' unreliable implicit implementation of state tracking and parsing algorithms rather than limitations in belief and counterfactual reasoning.

Clinical guidelines, typically developed by independent specialty societies, inherently exhibit substantial fragmentation, redundancy, and logical contradiction. These inconsistencies, particularly when applied to patients with multimorbidity, not only cause cognitive dissonance for clinicians but also introduce catastrophic noise into AI systems, rendering the standard Retrieval-Augmented Generation (RAG) system fragile and prone to hallucination. To address this fundamental reliability crisis, we introduce a Neuro-Symbolic framework that automates the detection of recommendation redundancies and conflicts. Our pipeline employs a multi-agent system to translate unstructured clinical natural language into rigorous symbolic logic language, which is then verified by a Satisfiability (SAT) solver. By formulating a hierarchical taxonomy of logical rule interactions, we identify a critical category termed Local Conflict - a decision conflict arising from the intersection of comorbidities. Evaluating our system on a curated benchmark of 12 authoritative SGLT2 inhibitor guidelines, we reveal that 90.6% of conflicts are Local, a structural complexity that single-disease guidelines fail to address. While state-of-the-art LLMs fail in detecting these conflicts, our neuro-symbolic approach achieves an F1 score of 0.861. This work demonstrates that logical verification must precede retrieval, establishing a new technical standard for automated knowledge coordination in medical AI.

RTL program repair remains a critical bottleneck in hardware design and verification. Traditional automatic program repair (APR) methods rely on predefined templates and synthesis, limiting their bug coverage. Large language models (LLMs) and coding agents based on them offer flexibility but suffer from randomness and context corruption when handling long RTL code and waveforms. We present Clover, a neural-symbolic agentic harness that orchestrates RTL repair as a structured search over code manipulations to explore a validated solution for the bug. Recognizing that different repair operations favor distinct strategies, Clover dynamically dispatches tasks to specialized LLM agents or symbolic solvers. At its core, Clover introduces stochastic tree-of-thoughts, a test-time scaling mechanism that manages the main agent's context as a search tree, balancing exploration and exploitation for reliable outcomes. An RTL-specific toolbox further empowers agents to interact with the debugging environment. Evaluated on the RTL-repair benchmark, Clover fixes 96.8% of bugs within a fixed time limit, covering 94% and 63% more bugs than both pure traditional and LLM-based baselines, respectively, while achieving an average pass@1 rate of 87.5%, demonstrating high reliability and effectiveness.

Code localization is a cornerstone of autonomous software engineering. Recent advancements have achieved impressive performance on real-world issue benchmarks. However, we identify a critical yet overlooked bias: these benchmarks are saturated with keyword references (e.g. file paths, function names), encouraging models to rely on superficial lexical matching rather than genuine structural reasoning. We term this phenomenon the Keyword Shortcut. To address this, we formalize the challenge of Keyword-Agnostic Logical Code Localization (KA-LCL) and introduce KA-LogicQuery, a diagnostic benchmark requiring structural reasoning without any naming hints. Our evaluation reveals a catastrophic performance drop of state-of-the-art approaches on KA-LogicQuery, exposing their lack of deterministic reasoning capabilities. We propose LogicLoc, a novel agentic framework that combines large language models with the rigorous logical reasoning of Datalog for precise localization. LogicLoc extracts program facts from the codebase and leverages an LLM to synthesize Datalog programs, with parser-gated validation and mutation-based intermediate-rule diagnostic feedback to ensure correctness and efficiency. The validated programs are executed by a high-performance inference engine, enabling accurate and verifiable localization in a fully automated, closed-loop workflow. Experimental results demonstrate that LogicLoc significantly outperforms SOTA methods on KA-LogicQuery while maintaining competitive performance on popular issue-driven benchmarks. Notably, LogicLoc attains superior performance with significantly lower token consumption and faster execution by offloading structural traversal to a deterministic engine, reducing the overhead of iterative LLM inference.

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.

Tabular data remains prevalent in high-stakes domains such as healthcare and finance, where predictive models are expected to provide both high accuracy and faithful, human-understandable reasoning. While symbolic models offer verifiable logic, they lack semantic expressiveness. Meanwhile, general-purpose LLMs often require specialized fine-tuning to master domain-specific tabular reasoning. To address the dual challenges of scalable data curation and reasoning consistency, we propose ReSS, a systematic framework that bridges symbolic and neural reasoning models. ReSS leverages a decision-tree model to extract instance-level decision paths as symbolic scaffolds. These scaffolds, alongside input features and labels, guide an LLM to generate grounded natural-language reasoning that strictly adheres to the underlying decision logic. The resulting high-quality dataset is used to fine-tune a pretrained LLM into a specialized tabular reasoning model, further enhanced by a scaffold-invariant data augmentation strategy to improve generalization and explainability. To rigorously assess faithfulness, we introduce quantitative metrics including hallucination rate, explanation necessity, and explanation sufficiency. Experimental results on medical and financial benchmarks demonstrate that ReSS-trained models improve traditional decision trees and standard fine-tuning approaches up to $10\%$ while producing faithful and consistent reasoning

Standard dense retrievers lack a native calculus for multi-atom logical constraints. We introduce Neuro-Symbolic Fuzzy Logic (NSFL), a framework that adapts formal t-norms and t-conorms to neural embedding spaces without requiring retraining. NSFL operates as a first-order hybrid calculus: it anchors logical operations on isolated zero-order similarity scores while actively steering representations using Neuro-Symbolic Deltas (NS-Delta) -- the first-order marginal differences derived from contextual fusion. This preserves pure atomic meaning while capturing domain reliance, preventing the representation collapse and manifold escape endemic to traditional geometric baselines. For scalable real-time retrieval, Spherical Query Optimization (SQO) leverages Riemannian optimization to project these fuzzy formulas into manifold-stable query vectors. Validated across six distinct encoder configurations and two modalities (including zero-shot and SOTA fine-tuned models), NSFL yields mAP improvements up to +81%. Notably, NSFL provides an additive 20% average and up to 47% boost even when applied to encoders explicitly fine-tuned for logical reasoning. By establishing a training-free, order-aware calculus for high-dimensional spaces, this framework lays the foundation for future dynamic scaling and learned manifold logic.

The generation of high-fidelity synthetic data is a cornerstone of modern machine learning, yet Large Language Models (LLMs) frequently suffer from hallucinations, logical inconsistencies, and mode collapse when tasked with structured generation. Existing approaches, such as prompting or retrieval-augmented generation, lack the mechanisms to balance linguistic expressivity with formal guarantees regarding validity and coverage. To address this, we propose CircuitSynth, a novel neuro-symbolic framework that decouples semantic reasoning from surface realization. By distilling the reasoning capabilities of a Teacher LLM into a Probabilistic Sentential Decision Diagram (PSDD), CircuitSynth creates a tractable semantic prior that structurally enforces hard logical constraints. Furthermore, we introduce a convex optimization mechanism to rigorously satisfy soft distributional goals. Empirical evaluations across diverse benchmarks demonstrate that CircuitSynth achieves 100% Schema Validity even in complex logic puzzles where unconstrained baselines fail (12.4%) while significantly outperforming state-of-the-art methods in rare-combination coverage.

Automating legal reasoning forces a choice between imperfect alternatives: symbolic systems offer transparency but struggle with ambiguity, whereas neural systems handle natural language flexibly but lack verifiability. This paper investigates whether a hybrid, neuro-symbolic approach can reconcile this trade-off. We evaluate this architecture in the domain of online content moderation, which serves as a proxy for high-volume legal decision-making such as mass administrative proceedings. In these settings, operators must assess thousands of cases daily under strict legal standards. Specifically, we examine whether constraining large language models (LLMs) within deterministic symbolic scaffolds improves statute-grounded illegality assessment while preventing "scope drift" (where LLMs conflate moral offensiveness with legal illegality). We evaluate the neuro-symbolic variant of Rulemapping - a visual logic-tree method that operationalises the classic legal syllogism - on online hate-speech classification under §130(1) of the German Criminal Code. Across diverse LLMs, Rulemapping maintains high recall (0.82-0.89) while achieving precision of 0.80-0.86, compared to 0.34-0.49 for unconstrained prompting. Expert-authored symbolic scaffolds thus enable robust legal automation aligned with regulatory requirements for auditability and verifiable decision-making.

Large language models increasingly operate under multiple instructions from heterogeneous sources with different authority levels, including system policies, user requests, tool outputs, and retrieved context. While prior work on instruction hierarchy highlights the importance of respecting instruction priorities, it mainly focuses on adversarial attacks and overlooks the benign but common instruction conflicts that arise in real-world applications. In such settings, models must not only avoid security violations but also preserve task utility and behavioral consistency when instructions partially or implicitly conflict. We propose Neuro-Symbolic Hierarchical Alignment (NSHA) for hierarchical instruction-following by explicitly modeling and enforcing instruction priorities. At inference time, we introduce solver-guided reasoning that formulates instruction resolution as a constraint satisfaction problem, enabling the model to derive a maximally consistent set of applicable instructions under hierarchical constraints. At training time, NSHA distills solver-based decisions into model parameters using automatically constructed supervision. We evaluate our approach on rule following, task execution, tool use, and safety, covering both single-turn and multi-turn interactions, and show that NSHA significantly improves performance under such conflicts while maintaining competitive utility in reference settings.

Learning rules plays a crucial role in deep learning, particularly in explainable artificial intelligence and enhancing the reasoning capabilities of large language models. While existing rule learning methods are primarily designed for symbolic data, learning rules from image data without supporting image labels and automatically inventing predicates remains a challenge. In this paper, we tackle these inductive rule learning problems from images with a framework called γILP, which provides a fully differentiable pipeline from image constant substitution to rule structure induction. Extensive experiments demonstrate that γILP achieves strong performance not only on classical symbolic relational datasets but also on relational image data and pure image datasets, such as Kandinsky patterns.

AI-driven symptom analysis systems face persistent challenges in reliability, interpretability, and hallucination. End-to-end generative approaches often lack traceability and may produce unsupported or inconsistent diagnostic outputs in safety-critical settings. We present SymptomWise, a framework that separates language understanding from diagnostic reasoning. The system combines expert-curated medical knowledge, deterministic codex-driven inference, and constrained use of large language models. Free-text input is mapped to validated symptom representations, then evaluated by a deterministic reasoning module operating over a finite hypothesis space to produce a ranked differential diagnosis. Language models are used only for symptom extraction and optional explanation, not for diagnostic inference. This architecture improves traceability, reduces unsupported conclusions, and enables modular evaluation of system components. Preliminary evaluation on 42 expert-authored challenging pediatric neurology cases shows meaningful overlap with clinician consensus, with the correct diagnosis appearing in the top five differentials in 88% of cases. Beyond medicine, the framework generalizes to other abductive reasoning domains and may serve as a deterministic structuring and routing layer for foundation models, improving precision and potentially reducing unnecessary computational overhead in bounded tasks.

We present a neurosymbolic approach, i.e. combine symbolic and subsymbolic artificial intelligence, to validating offer documents in regulated public institutions. We employ a language model to extract information and then aggregate it with an LTN (Logic Tensor Network) to make an auditable decision. In regulated public institutions, decisions must be made in a manner that is both factually correct and legally verifiable. Our neurosymbolic approach allows existing domain-specific knowledge to be linked to the semantic text understanding of language models. The decisions resulting from our pipeline can be justified by predicate values, rule truth values, and corresponding text passages. Our experiments on a real corpus show that the proposed pipeline achieves performance comparable to existing models, but its key advantage lies in its interpretability, modular predicate extraction, and explicit support for XAI (Explainable AI).

As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some neurosymbolic systems verify claims by using LLMs to translate natural language into logical formulae and then checking whether the proposed claims are logically sound, i.e. whether they can be validly derived from premises that are verified to be true. We argue that such approaches structurally fail to detect misleading claims due to systematic divergences between conclusions that are logically sound and inferences that humans typically make and accept. Drawing on studies in cognitive science and pragmatics, we present a typology of cases in which logically sound conclusions systematically elicit human inferences that are unsupported by the underlying premises. Consequently, we advocate for a complementary approach: leveraging human-like reasoning tendencies of LLMs as a feature rather than a bug, and using these models to validate the outputs of formal components in neurosymbolic systems against potentially misleading conclusions.

Large language models (LLMs) have demonstrated strong potential in long-horizon decision-making tasks, such as embodied manipulation and web interaction. However, agents frequently struggle with endless trial-and-error loops or deviate from the main objective in complex environments. We attribute these failures to two fundamental errors: global Progress Drift and local Feasibility Violation. Existing methods typically attempt to address both issues simultaneously using a single paradigm. However, these two challenges are fundamentally distinct: the former relies on fuzzy semantic planning, while the latter demands strict logical constraints and state validation. The inherent limitations of such a single-paradigm approach pose a fundamental challenge for existing models in handling long-horizon tasks. Motivated by this insight, we propose a Neuro-Symbolic Dual Memory Framework that explicitly decouples semantic progress guidance from logical feasibility verification. Specifically, during the inference phase, the framework invokes both memory mechanisms synchronously: on one hand, a neural-network-based Progress Memory extracts semantic blueprints from successful trajectories to guide global task advancement; on the other hand, a symbolic-logic-based Feasibility Memory utilizes executable Python verification functions synthesized from failed transitions to perform strict logical validation. Experiments demonstrate that this method significantly outperforms existing competitive baselines on ALFWorld, WebShop, and TextCraft, while drastically reducing the invalid action rate and average trajectory length.