Neuro-Symbolic Reasoning

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11 papers in the last four weeks, up 57% on the four weeks before. 0.1% of all new papers.

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Jul 31, 2026cs.LG

A Neurosymbolic Approach for Explainable Early Diagnosis of Alzheimer's Disease

Identifying reliable Alzheimer's disease (AD) markers typically requires manual, labor-intensive transcription and expert analysis, limiting its scale. We introduce an automated pipeline that extracts qualitative knowledge about potential AD progression indicators directly from audio recordings of verbal fluency tests. Our method uses pretrained foundation models to process raw audio and extract clinically relevant variables to construct a Bayesian Network (BN); this BN is used to reason about the AD progression markers and infer their qualitative relationships. Our system successfully recovers known clinical knowledge and identifies novel relationships between linguistic markers.

Ranveer Singh, Pranuthi Tenali, Saurabh Mathur +6

The University of Texas at Dallas, Richardson, TX · TU Darmstadt, Germany · Swarthmore College, PA +1

Alzheimer's Disease Interpretable ML Speech-Based Dementia Detection Neuro-Symbolic Reasoning

Jul 31, 2026cs.AI

NeSyFS: A Neuro-symbolic Fast-Slow Thinking Framework for LLM Agent under Partial Observability

Recently Large Language Models (LLMs) have been increasingly deployed as autonomous agents in applications such as self-reflection, retrieval-augmented generation, and scientific discovery. In these settings, agents must act based on limited observations rather than full environmental states, leading to partial observability. This introduces several key challenges: belief state inference, task objective misalignment, and planning under uncertainty. Prior approaches typically condition actions on full or summarized action-observation histories whose redundant and irrelevant information can mislead the decision making of LLM agent. Inspired by human cognition, we propose a novel neuro-symbolic fast-slow thinking (NeSyFS) framework for LLM agent, addressing the challenges introduced by partial observability in a unified approach. We use a knowledge graph (KG) to represent the belief state, providing triplets as context for every module of NeSyFS. The fast-thinking module performs reactive action, while slow-thinking conducts a new uncertainty-aware planning by following the high-level structure of twisted sequential Monte Carlo (TSMC) algorithm. To mitigate the misalignment of task objective, a reflection module is used to reflect fast-thinking actions, and also switches to the slow-thinking module whenever reactive actions repeatedly fail. Experiments on three representative benchmarks, i.e. ALFWorld, Webshop, and ScienceWorld, demonstrate significant advantages over previous methods.

Duo Xu, Faramarz Fekri

Georgia Institute of Technology 225 North Ave NW, Atlanta, GA 30332

Belief-Space Planning LLM Agents Neuro-Symbolic Reasoning LLM Agent Planning

Jul 30, 2026cs.AI

A Fuzzy Rule-based Neuro-Symbolic Approach for Pipe Severity Prediction in Sewer Networks

Standard automated sewer pipe severity assessment relies on direct image classification, creating a "black box" where the link between visual defects and final severity scores remains implicit. This study introduces a modular, fuzzy rule-based neuro-symbolic framework that bridges this gap by decoupling neural perception from symbolic reasoning. The perception module utilizes a Swin Transformer to predict 14 multilabel inspection CODE degrees directly from images. For reasoning, a DT, specifically Weka's J48, algorithm is trained on ground-truth CODEs and severity labels, and its paths are converted into 19 fixed IF--THEN rules. Inference operates via fuzzy logic: t-norm activations from CODE conditions are weighted by rule confidence and combined with corresponding s-norms to produce interpretable class evidence. We assessed Product, Łukasiewicz, and Hamacher operator pairs using a dataset of 3,244 images spanning five highly imbalanced severity classes. Ground-truth labels were robustly generated via consensus from five independent large language models analyzing original inspector notes. Our results show an improvement of accuracy, balanced accuracy, Macro F1 and MCC by 17.9%, 12.2%, 23.0%, and 17.3%, respectively, over image-only based classification. Overall, the framework combines competitive class-balanced performance with traceable reasoning from predicted CODE degrees to rule supports and severity evidence.

Ngoc Thai Le, Thanh Ma, Umberto Straccia

Can Tho University, Can Tho, Vietnam · Istituto di Scienza e Tecnologie dell’Informazione, CNR - ISTI, Pisa, Italy

Fuzzy Logic Neuro-Symbolic Reasoning Structural Health Monitoring

Jul 30, 2026cs.AI

Distilling Answer Set Programming Theories from Large Language Models

Writing Answer Set Programming (ASP) theories from scratch is a difficult and time-consuming task. We take a neurosymbolic approach to study whether a model can distill complete and correct theories, given a fixed agent harness with the solver in the loop. The protocol is dataset-agnostic: with a single prompt and an empty file as the starting point the model is given a 1-hour time limit to derive a complete theory. We chose VQA as the application domain, three benchmarks (CLEVR, GQA, CLEVRER), as these are publicly available and non-trivial. In order to study the model scale required for solving this task we nine different models: four frontier (Claude Sonnet 4.6, Claude Opus 4.7, GPT-5, DeepSeek V4 Pro), two mid-tier (DeepSeek V4 Flash, gpt-oss-120b), and three open-weights (qwen3.6-27b, gpt-oss-20b, qwen3.5-9b). Three of four frontier models reach 100% on CLEVR and 92.8%-98.8% on GQA; on CLEVRER, Sonnet, Opus, DeepSeek V4 Pro score 92.7%-95.3%. GPT-5 reaches 98.7% on CLEVR but drops to 41.8% on GQA and to 86.7% on CLEVRER. Adding handwritten reference theories from other datasets moves the other three frontier models by at most +/-3.4 pp but reduces GPT-5's accuracy by 3-19 pp. We release the code, prompts, and theories distilled.

Nelson Higuera Ruiz, Markus Hofmarcher, Claudiu Leoveanu-Condrei

ExtensityAI, Vienna, Austria

Logic Programming LLM-Based Program Synthesis Answer Set Programming Neuro-Symbolic Reasoning Knowledge-Based VQA

Jul 29, 2026cs.CV

From Pixels to PCells: A Neurosymbolic Approach to Photonic Component Creation

We present PixCell, a neurosymbolic system in which multimodal agents convert a visually presented photonic component into a parametric program over a small domain-specific language (DSL) of geometric primitives. A system enabling deterministic visual verification renders evaluation asymmetrically cheaper than the generation attempt. While models using multi-seed sampling and iterative revision reach a mean best-turn IoU of only 0.416, multimodal agents through PixCell's interface and verifier consistently exceed 0.9 mean IoU, with scores reaching 0.974 and 0.955 across eight component targets while also satisfying source contracts. These results demonstrate that frontier multimodal agents can reliably understand and render executable parametric representations from visual targets. Using these live parameters, cross-stack studies on an interferometer reconstruct primitive programs that satisfy an 8.0 nm free spectral range target and the original footprint constraint on modeled 220-nm SOI, 400-nm SiN, and 400-nm TFLN stacks. PixCell further carries a paper-derived splitter from visual reconstruction through SOI full-wave simulation, producing symmetric propagation and balanced outputs. Finally, the same executable verifier supplies a training reward and dataset used to train a Qwen3.6-35B-A3B model with LoRA and GRPO without supervised demonstrations. On eight training-excluded paper figures, its mean champion IoU rises from 0.422 after eight initial attempts to 0.491 after three verifier-guided revision rounds. These results therefore establish a controlled framework for measuring, retargeting, and improving visual-to-parametric photonic component design.

Aadarsh Agarwal, Kenaish Al Qubaisi, Dirk Englund

Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

LLM-Based Program Synthesis Program Synthesis Neuro-Symbolic Reasoning Multimodal Agents

Jul 25, 2026cs.AI

SymStep: Symbolic Step Verification for Logical Reasoning

Chain-of-thought (CoT) prompting can fail severely on constraint-dense logical reasoning tasks, where unverified errors accumulate silently across steps. We introduce SymStep: an LLM makes one atomic claim at a time (DEDUCE: Alice, pet, Cat), then a lightweight constraint propagator checks the claim for consistency with prior accepted deductions, rejects contradictions, and cascades implied facts automatically. SymStep+G additionally provides MRV guidance after each accepted step, directing the LLM toward the most constrained unresolved variable. On a 35-puzzle retained subset of ZebraLogicBench, a benchmark of 1,000 Einstein-style logic puzzles, Direct and CoT both achieve 0%, while SymStep+G reaches 97%. On AR-LSAT analytical reasoning problems, SymStep achieves 100% vs. CoT's 87%. On LGP-14, SymStep+G achieves 100% vs. 0% for CoT and Logic-LM, the strongest prior symbolic+LLM baseline we compare against. Ablation studies reveal that MRV guidance is a key mechanism for reducing directionless cycling, while consistency checking provides a safety net against explicit contradictions. Across six benchmarks spanning five task domains, SymStep variants match or exceed every baseline on constraint-dense and arithmetic tasks. Experiments on AQUA-RAT algebra confirm the advantage is constraint-density-specific.

Aida Usmanova, Rui Gao, Dilshod Azizov +2

Leuphana University of Lüneburg · Mohamed bin Zayed University of Artificial Intelligence

Symbolic Reasoning Structured Reasoning Neuro-Symbolic Reasoning Constraint Satisfaction LLM Reasoning

Jul 25, 2026cs.AI

Reason Popper-ly: Patching In-Context Reasoning with Inductive Logic Programming

Chain-of-thought (CoT) prompting enables large language models (LLMs) to tackle multi-step reasoning tasks, yet the generated intermediate steps are not guaranteed to be logically sound. We present Reason Popper-ly, a neurosymbolic framework that uses inductive logic programming (ILP) to learn relation composition rules from reasoning traces and deploys them as an online verifier for step-level correction. Given an LLM-generated trace, the method checks each inferred step against the learned rule table, diagnoses the violation type, rewrites incorrect steps with symbolically derived repairs, and regenerates the remaining suffix so that the model can produce its final answer conditioned on a verified trace. We evaluate on CLUTRR, a multi-hop kinship reasoning benchmark, using five language models over reasoning chains of 2 to 10 hops. Across all models, Reason Popper-ly consistently improves terminal accuracy over standard CoT, with gains of up to 48 percentage points for small models and 15 points for frontier models on the longest chains. Compared with a fully exogenous symbolic pipeline, our method performs better on harder instances by preserving the model's successful grounding while correcting only verifiable reasoning failures. In addition, step-level ILP verification yields a fine-grained error taxonomy that provides diagnostic insight beyond final-answer accuracy.

Zirong Chen, Meiyi Ma

Department of Computer Science, Vanderbilt University, USA

Logic Programming Reasoning Consistency in Language Models Structured Reasoning Neuro-Symbolic Reasoning Inductive Logic Programming Multi-Hop Reasoning+1

Jul 23, 2026cs.AI

Euclid-MCP: A Model Context Protocol Server for Deterministic Logical Reasoning via Prolog

Large Language Models (LLMs) excel at natural language understanding and generation but remain unreliable for multi-step logical reasoning, especially in safety-critical or compliance-sensitive domains. Recent neuro-symbolic approaches address this gap by coupling neural models with external symbolic engines, yet most integrations are bespoke and lack a standardized interface for tool-augmented agents. This paper presents Euclid-MCP, an open-source MCP server that provides deterministic logical reasoning via SWI-Prolog. Euclid-MCP introduces Euclid-IR, an engine-agnostic intermediate representation for Horn-clause logic that is human-readable, easy for LLMs to generate, and straightforward to compile into Prolog or alternative backends. The server exposes a compact tool interface that supports a translate-run-inspect-repair loop, enabling LLM clients to delegate inference while retaining full access to proof traces and derivation logs. We evaluate Euclid-MCP on a realistic IT security and compliance use case. Results show that while LLMs alone are sufficient on small knowledge bases, they hallucinate systematically on larger problems, whereas Euclid-MCP delivers exact answers with lower latency and more compact outputs. We argue that semantic RAG is fundamentally unsuited for rule enforcement, and that Euclid-MCP can serve as a stable, shared reasoning substrate for both RAG-based assistants and agentic systems.

Bartolomeo Bogliolo

Logic Programming LLM Reliability Model Context Protocol Neuro-Symbolic Reasoning LLM Reasoning

Jul 23, 2026cs.AI

Differentiable Logic Programming to Mitigate Reasoning Shortcuts in Neurosymbolic Systems

Neurosymbolic (NeSy) systems integrate neural networks with logical reasoning to achieve both generalization and interpretability, but recent work has shown they are susceptible to shortcut reasoning behaviors. We propose a novel method using matrix-based differentiable logic programming to mitigate reasoning shortcuts in two phenomena: constraint satisfaction shortcuts, where constraints are satisfied without achieving the intended task, and cognition shortcuts, where biased data leads to semantically incorrect concept mappings despite logically sound inference. Building on recent matrix-based logic programming semantics, we introduce design elements to mitigate shortcuts, including a unified encoding of rules and constraints in a single matrix. We also identify connections to fuzzy logic t-norms and empirically compare their gradient flow properties. Through carefully designed experiments on MNIST variants, we show that one-to-one grounding of neural outputs to logical atoms significantly reduces both shortcut types compared to previous methods that rely on soft probability distributions. We then confirm that architectural choices in coupling symbolic knowledge with neural learning play a critical role in shortcut mitigation.

Akihiro Takemura, Katsumi Inoue

National Institute of Informatics, Tokyo, Japan

Differentiable Programming Neuro-Symbolic Reasoning

Jul 22, 2026cs.AI

SoftReason: A Fully Differentiable Neuro-Soft-Symbolic Deductive Reasoning Architecture over High-Dimensional Perceptual Data

In many reasoning problems, the premises are not observed as discrete symbols, but must be inferred from high-dimensional inputs. Further, the predicate vocabulary, argument structure, and trusted evidence are supplied by a Knowledge Graph (KG), or rule definitions. Classical neuro-symbolic pipelines have a discrete interface between perception and deduction. We present a neuro-soft-symbolic architecture for differentiable deductive reasoning over latent perceptual facts and knowledge-provided predicates. SoftReason removes the gradient gap by representing the deductive state as a local soft interpretation tensor over candidate constants and predicates. Perception proposes probabilistic base facts, KG triples enter as high-confidence soft evidence, and every query anchor, predicate choice, and closure update remains differentiable. Our core innovation is a learned differentiable lift of the immediate-consequence operator. It uses predicate-definition embeddings and latent composition channels to form soft body-predicate mixtures, aggregate over all possible witnesses, propose query-conditioned head facts, and update the interpretation through a monotone probabilistic OR. We instantiate the framework on Knowledge-aware Visual Question Answering (KVQA), and demonstrates how SoftReason supports end-to-end perceptual grounding, KG evidence injection, and differentiable deductive closure in one trainable architecture.

Wael AbdAlmageed

Holcombe Department of Electrical and Computer Engineering, Clemson University

Visually Grounded Reasoning Neuro-Symbolic Reasoning Knowledge-Based VQA

Jul 20, 2026cs.AI

Neuro-Symbolic Meta-Policies for Temporal Knowledge-Graph Memory under Partial Observability

Partially observable reinforcement learning requires deciding what to retain, retrieve, and forget over time. We introduce a neuro-symbolic meta-policy that learns which symbolic memory heuristic to apply at each decision point while keeping execution symbolic. Our setting uses temporal knowledge-graph memory in RoomKG, where hidden state and observations are represented as Resource Description Framework (RDF) graphs and memory is augmented with temporal RDF triple annotations. The model combines knowledge-graph encoding of memory contents with value heads for question answering, exploration, and forgetting, yielding a controller that is both adaptive and inspectable. This gives the work a direct Semantic Web grounding through RDF-based representation, annotation-compatible graph semantics, and graph-based symbolic operations over explicit memory state. On train/test room splits at long-term memory capacity of 512, the qualifier-aware StarE-GNN configuration achieves the best held-out performance among the compared symbolic, neural, and neuro-symbolic systems while preserving step-level traceability of memory-management decisions.

Taewoon Kim, Vincent François-Lavet, Michael Cochez

HumemAI, The Netherlands · Vrije Universiteit Amsterdam, The Netherlands · ELLIS Institute Finland & Abo Akademi University, Finland

Reinforcement Learning Partially Observable RL Graph-Based Agent Memory Meta-Reinforcement Learning Neuro-Symbolic Reasoning Memory-Augmented Agents

Jul 18, 2026cs.AI

Constraint-Anchored Reasoning Traces

Autoregressive multimodal large language models (MLLMs) suffer from error snowballing: a single incorrect inference early in a chainof-thought (CoT) trace corrupts all downstream reasoning. We find that in state-of-the-art open-source MLLMs, once the first error occurs, the reasoning cascades into failure across all remaining steps in 65% of such cases (a metric we term the snowball rate). Existing mitigations-sampling multiple chains, post-hoc self-verification, or full program synthesis-either lack symbolic grounding, catch errors too late, or sacrifice the flexibility of natural language reasoning. We propose Constraint-Anchored Reasoning Traces (CART), a neuro-symbolic framework that trains MLLMs to interleave natural language reasoning steps with symbolic constraint assertions: lightweight, machine-checkable statements about visual content (e.g., count(red_objects) = 3). A dual-pronged Constraint Propagation Module-combining a learned neural grounding head with Boolean Constraint Propagation-continuously verifies these anchors against extracted visual features and checks their mutual logical consistency. When a contradiction is detected, a backtrack controller halts generation and reverts to the last consistent checkpoint, preventing error propagation. A variable-frequency emission mechanism allows the model to adaptively control anchor density, avoiding trace bloat. We construct 218K training instances by augmenting GQA, CLEVR-CoGenT, and VCR with ground-truth constraint annotations derived from scene graphs, and fine-tune open-source MLLMs (LLaVA-NeXT, Qwen2-VL) via LoRA. On five benchmarks, CART reduces the snowball rate from 0.65 to 0.14, improves GQA accuracy by +4.6 percentage points over trainingonly baselines, and achieves 89.1 F1 on POPE-all with at most 18% inference overhead.

Zehua Cheng, Wei Dai, Jiahao Sun

Department of Computer Science University of Oxford United Kingdom · FLock.io United Kingdom

Visual Question Answering LLM Grounding Multimodal CoT Reasoning Neuro-Symbolic Reasoning

Jul 17, 2026cs.AI

NeurOWL: An LLM-Based Neural-symbolic Framework for Incomplete OWL Ontology Reasoning

OWL ontologies provide a formal knowledge representation framework that enables semantic reasoning, and have been widely adopted across domains such as healthcare and bioinformatics. In practice, however, real-world ontologies are often incomplete, which pose challenges for reasoning. In this work, we focus on a fundamental subsumption reasoning problem: given an incomplete ontology and a candidate (non-entailed) subsumption, determine whether the subsumption is semantically plausible and, if so, providing a logically sound explanation containing potential missing axioms. This task unifies subsumption verification with ontology abduction, and generalizes the latter by removing the need for a predefined candidate set of missing axioms. To address this subsumption reasoning problem, we propose NeurOWL, an end-to-end neuro-symbolic framework that jointly performs verification and abduction, leveraging both formally defined semantics and textual semantics through Large Language Models and ontology embeddings. We evaluate NeurOWL on real-world ontologies across multiple domains, demonstrating strong and robust performance across different domains.

Hui Yang, Jiaoyan Chen, Yiping Song +2

The University of Manchester · Zhejiang University

Logical Reasoning Abductive Reasoning Symbolic Reasoning Neuro-Symbolic Reasoning

Jul 16, 2026cs.CL

CoTu at EXACT 2026: Neuro-Symbolic Reasoning for Transparent Educational QA

Transparent educational question answering asks for answers that are not only correct but explainable, and doing so with small models rules out the reasoning power of the largest proprietary systems. The EXACT 2026 competition poses this problem concretely: open-weight language models of at most 8B parameters, self-hosted, with a natural-language explanation for every answer. It pairs two tasks: logical reasoning over university regulations, and multi-step physics problem solving. We describe the system that team \cotu{} developed to address both, a neuro-symbolic Program-of-Thought pipeline in which a 4B backbone writes a program rather than stating an answer directly: for regulation queries it emits a Z3 encoding whose entailment verdict grounds the deduction, and for physics it emits numerical Python, both wrapped in a shared self-correction loop and a unified explained-JSON output. Answer-type routing, distillation-based task fine-tuning, and a latency-aware serving stack -- SGLang with speculative decoding -- keep the system within the 60-second per-query limit. The system achieved a \textbf{perfect score} on the physics task in both automated selection rounds and obtained the \textbf{highest final-round technical score} of any team --

13.44/15

, combining automated answer evaluation with expert-judged reasoning depth -- with the equally weighted presentation score included, \cotu{} placed 3rd overall. Grounding answers in a symbolic solver yields correct, verifiable deductions at the 4B scale, and the residual difficulty lies in premise selection rather than the deduction itself.

Quoc-Khang Tran, Minh-Thien Nguyen, Phu-An Thai +3

Can Tho University, Can Tho city, Vietnam · Tay Do University, Can Tho city, Vietnam

Explainable Artificial Intelligence LLM-Based Program Synthesis Question Answering Structured Reasoning Neuro-Symbolic Reasoning LLM Mathematical Reasoning

Jul 14, 2026cs.AI

MaxSAT-Based Feedback for Guiding Vision-Language Models in Sudoku

Vision--Language Models (VLMs) have recently demonstrated promising performance on structured visual reasoning tasks, including grid-based puzzles. However, despite strong perceptual capabilities, these models lack explicit mechanisms for enforcing logical consistency and frequently generate assignments that violate underlying constraints. In this paper, we propose a neuro-symbolic approach that integrates formal constraint reasoning into the VLM solving process via a Maximum Satisfiability (MaxSAT) oracle. Rather than computing solutions directly, the symbolic component acts as a consistency validator and refinement engine. Candidate placements generated by the VLM are encoded as soft clauses in a partial MaxSAT formulation, while Sudoku constraints remain hard clauses. When inconsistencies arise, the MaxSAT solver identifies a largest mutually consistent subset of assignments, which is then translated into structured textual and visual feedback to guide subsequent refinements. We evaluate our approach on a Sudoku dataset across multiple open-source and closed-access VLMs. Results show that MaxSAT-based feedback improves logical consistency and increases the number of solved instances, particularly in full-board refinement mode. These findings demonstrate that symbolic optimisation can enhance the reliability of vision-language reasoning.

Pedro Orvalho, Guillem Alenyà, Felip Manyà

Artificial Intelligence Research Institute (IIIA), Consejo Superior de Investigaciones Científicas (CSIC), Barcelona, Catalonia, Spain · Institut de Robòtica i Informàtica Industrial (IRI-CSIC-UPC), Barcelona, Spain

Vision-Language Models VLM Reasoning Neuro-Symbolic Reasoning Constraint Satisfaction Maximum Satisfiability

Jul 13, 2026cs.AI

AutoVSR: Automatic Visual-to-Symbolic Reasoning for Symbolic Expression Generation from Circuit Schematic

Symbolic expressions can effectively characterize and predict circuit behavior, but deriving them directly from circuit schematics is challenging. This process requires accurate visual-to-symbolic construction of circuit structure from images and correct multi-step symbolic derivation, both of which impose strict correctness requirements. This work proposes AutoVSR, an automated framework for visual-to-symbolic generation of circuit expressions using Vision Language Models (VLMs). By reconstructing circuit diagrams into an executable intermediate representation (Executable IR) and leveraging a symbolic solver for reasoning, AutoVSR significantly improves the accuracy of symbolic expression generation. AutoVSR introduces two key innovations: an IR construction method guided by component rule retrieval and verification-based feedback, and a symbolic solver implemented as a planning agent equipped with a symbolic tool library for reliable multi-step derivation. Compared with end-to-end VLM approaches and specialized methods on the main symbolic expression generation task, AutoVSR achieves accuracy improvements of 30.01--59.45% and 41.96--51.84%, respectively. Moreover, AutoVSR surpasses closed-source state-of-the-art VLMs in inference cost and computational efficiency. Code is available at https://github.com/LongfeiLi1/AutoVSR.

Zhe Xiao, Longfei Li, Xu He +3

Hunan University, Changsha, China · Wuhan University of Technology, Wuhan, China · Huazhong University of Science and Technology, Wuhan, China.

Electronic Design Automation VLM Reasoning Neuro-Symbolic Reasoning

Jul 12, 2026cs.AI

Probabilistic Extension of Neuro-Symbolic AGI Robots based on Belnap's Typed Intensional FOL

Neuro-symbolic AI based on

IFOL_B

is a way to combine neural learning and symbolic reasoning to overcome limitations of purely neural systems (like lack of interpretability and logical structure) with formal logical machinery for self-reference. In this paper we expand the cognitive power of

IFOL_B

by using the probability computation for the currently unknown sentences, based on Nilsson's probability structure for the

IFOL_B

. We introduce the global symmetry transformation that preserves the current knowledge database and logical deduction, and the local one used for real-time decisions about concrete (sub)problems that involve only a very strict subset of

IFOL_B

predicates. The computation of probability density function

KI

in both cases, based on the Shannon's maximum information entropy, is provided by neural networks of this probabilistic neuro-symbolic AGI.

Zoran Majkic

ISRST, Tallahassee, FL, USA

Probabilistic Logic Logical Reasoning Neuro-Symbolic Reasoning Neuro-Symbolic AI

Jul 10, 2026cs.AI

A Symbolic Neural CPU for Quantization-Simulated Writeback and Interpretable Program Execution

Neural networks can learn algorithmic input-output mappings, but trusting a learned executor requires more than a correct final answer because the state transitions that produce it are usually hidden. To make those transitions visible, we introduce a trace-supervised symbolic neural CPU, a factorized learned execution architecture that combines recurrent control, an explicit operation router over a fixed differentiable arithmetic-logic unit bank, destination-masked register writeback, complete trajectory supervision and matched fixed-point replay. The model exposes the selected operation, source and destination registers, register trajectory, memory signals and writeback semantics at every step. On the principal 16-wide benchmark, the non-quantized executor reproduces reference execution exactly, while the eight-bit quantization-simulated executor preserves the symbolic operation path through programs of 1,000 instructions. When the same execution is evaluated against a matched fixed-point replay, the residual numerical drift disappears, showing that it comes from a mismatch between continuous and low-precision reference semantics rather than from execution failure. We compare recurrent, Transformer, temporal-convolution, temporal graph-inspired and state-space controllers, and the ablations show that operation-gate supervision is necessary for an inspectable execution path. Hidden-opcode memory-pressure tasks expose the remaining limits in delayed state use and temporal binding. We also extend the interface with ValueMemory, hybrid adaptive leaky integrate-and-fire controllers, candidate-constrained symbolic control trained through behaviour cloning and actor-critic reinforcement learning, and an RV32I base-integer semantic bridge. Together, these results establish a trace-verifiable framework for interpretable, low-precision and controllable neural execution.

Jose Luis Lima de Jesus Silva

Federal University of Bahia, Department of Geophysics, Salvador, BA 40170-115, Brazil · Grupo de Estudos e Aplicação de Inteligência Artificial em Geofísica (GAIA), Federal University of Bahia, Salvador, BA 40170-115, Brazil

Neural Algorithmic Reasoning Neural Network Interpretability Neuro-Symbolic Reasoning Algorithmic Reasoning

Jul 9, 2026cs.AI

Answer Set Programming Energised! End-to-End Neurosymbolic Reasoning and Learning with ASP and Energy Based Models

We present a general neurosymbolic reasoning and learning methodology based on a modular integration of answer set programming with an energy based model substrate. Key contributions are: (1) supporting joint optimisation in the continuous latent space through explicit ASP-based declarative semantics fully incorporating background knowledge, constraints, non-monotonic inference; and (2) advancing recent works at the interface of answer sets, probabilistic logic, and answer set modulo theories by providing a generalised model and practical platform for ASP-centric robust, end-to-end training for applications in dynamic domains (e.g., involving perception and interaction). We provide a practical implementation, and demonstrate basic use and application (with MNIST), and evaluate with the visual question-answering benchmark Clevr and the multi-object tracking benchmark MOT.

Jakob Suchan, Julius Monsen, Salim Baloch +1

Constructor University Bremen, Bremen, Germany · CoDesign Lab > Cognitive Vision · Örebro University, Örebro, Sweden

Energy-Based Models Answer Set Programming Neuro-Symbolic Reasoning Neurosymbolic Learning

Jul 7, 2026cs.RO

EvoPlan: Evolutionary Neuro-Symbolic Robot Planning with Spatio-Temporal Guarantees

LLM-based robot planners are fluent but cannot guarantee that their plans are executable or safe. Classical PDDL planners can guarantee these properties, but only after the problem is fully specified, and they make poor use of an LLM's ability to read context and repair plans. This paper presents a neuro-symbolic framework with three parts. All LLM calls use a locally-hosted open-weight model, so the pipeline can be deployed on-robot with no cloud dependency. First, an offline procedure that mines a single global Signal Temporal Logic (STL) constraint on mobility from demonstration data. The procedure recovers codified rules (e.g., stopping at red lights, mined from nuPlan driving logs) or population preferences (e.g., social-navigation comfort, mined from SCAND teleoperation), depending on what the demonstrations encode. Because the demonstrations are a one-class signal, we generate the missing negatives with counterfactual perturbations and an LLM violation generator and then fit the constraint by evolutionary search. We use the mined constraint to shield a vision-language driving policy on Bench2Drive and two discrete-action navigation policies on HA-VLN-CE. Second, an evolutionary PDDL planner: an LLM proposes and repairs plans, programmatic validators decide which ones survive, and the validated portion of the plan grows over iterations. We test the planner on the open-world ALFWorld Text benchmark, where it beats strong baselines and stays robust when the goal vocabulary does not match the action-model vocabulary. Third, a constrained execution loop: the planner's plan is compiled into waypoints, the waypoints are checked against the mined constraint, and the planner re-plans on a violation. We illustrate the full pipeline via demonstrations using the Gazebo simulator.

Bhavya Sai Nukapotula, Samin Moosavi, Haoze Wang +4

Texas A&M University · Westwood High School

Constrained Motion Planning Large Language Model-Based Robot Planning Signal Temporal Logic Robot Safety Robot Task Planning Safe Motion Planning+1

Jul 6, 2026cs.AI

ClassicLogic: A Knowledge-Driven Benchmark of Classic Puzzle Games for Evaluating Compositional Generalization

Compositional generalization, the ability to understand and produce novel combinations of known components, remains a fundamental challenge for modern artificial intelligence. While few benchmarks exist, many focus on linguistic tasks and lack complex, explicit compositional structures. We introduce ClassicLogic, a new benchmark suite designed to evaluate an agent's ability to learn and compose problem-solving strategies. The benchmark consists of four classic logic puzzles: Sudoku, KenKen, Kakuro, and Futoshiki. Its core innovation is a hierarchical, explicit knowledge base for each game, where complex solving strategies are formally defined as compositions of simpler, foundational strategies. This structure allows for fine-grained evaluation of an agent's reasoning capabilities, from learning basic rules to applying multi-step compositional strategies to solve puzzles of increasing, mathematically validated difficulty. The open-source benchmark provides a challenging new testbed for advancing neuro-symbolic and other advanced AI reasoning systems.

Mahnoor Shahid, Hannes Rothe

Universität Duisburg-Essen Germany

Logical Reasoning Benchmark Design Neuro-Symbolic Reasoning Algorithmic Reasoning Compositional Generalization

Jul 5, 2026cs.AI

Forethought: Verifiable Reasoning from Neurosymbolic Primitive Programming

Current agentic workflows usually involve decomposing user requests into sequences of tool calls with correctly resolved parameters, the results of which are processed through reasoning traces in the language model's context window. The prevailing route to improve such reasoning is test-time scaling, which trains models to search over long chains of thought; but the resulting capability is entangled in model weights, is not verifiable step-by-step, and is costly at inference. We present Forethought, a neurosymbolic reasoning system that instead treats reasoning as an explicit, verifiable program, that builds from a library of symbolic and neural primitives which are composed through a domain-specific language. The result are reasoning programs, which are concrete representations of the model's work, and as such can be inspected and modified before deployment. Instantiated as a tool-calling execution kernel and evaluated across five benchmarks, Forethought improves base-model accuracy by about 30% relative and outperforms vanilla prompting, reinforcement learning scaffolds, and prompt-evolution methods, enabling small models to match or exceed frontier models capabilities. In a direct comparison, a non-reasoning model augmented with Forethought competes with a dedicated reasoning model while requiring roughly three orders of magnitude less post-training investment, and remains model-agnostic and auditable.

Vishvesh Bhat, Jay Vaghasiya, Emmanuel Anaya Gonzalez

CoreThink AI · UC San Diego

Symbolic Reasoning Efficient Language Model Reasoning Agentic Reasoning LLM Tool Use Neuro-Symbolic Reasoning

Jul 4, 2026cs.LG

NeSy-CSA: A Neuro-Symbolic Framework for Open-Ended Critical Scenario Attribution

Understanding why discovered scenarios become critical in scenario-based testing is essential for effectively leveraging them in decision-making systems. Reasoning about such criticality can be formulated as an attribution problem. However, across different decision-making tasks, the causes of criticality may involve diverse state variables, interaction patterns, and failure mechanisms, making attribution an inherently open-ended problem beyond predefined explanation spaces. Existing attribution methods still struggle to balance open-ended reasoning flexibility with the interpretability and traceability required for critical scenario reasoning. To address this limitation, we propose NeSy-CSA, a neuro-symbolic framework that transforms open-ended critical scenario attribution from unconstrained explanation generation into structured and traceable reasoning. NeSy-CSA narrows the attribution space by selecting relevant factors, makes the reasoning process traceable through a dependency-aware evidence graph, and executes symbolic reasoning procedures derived from atomic operations, coordinated with evidence-constrained neural inference to support flexible open-ended attribution. We further introduce a process-level and result-level assessment module to evaluate the structural validity of the attribution process and the behavioral effectiveness of the attribution results under controlled interventions. Experiments across four decision-making environments show that NeSy-CSA improves two intervention-based measures of attribution effectiveness by 18.32% and 13.67% over LLM-based baselines. These results demonstrate its potential to transform discovered critical scenarios into reusable knowledge for subsequent testing and safety analysis.

Qitong Chu, Xunjie He, Chen Deng +2

School of Automation, Beijing Institute of Technology, Beijing 100081, China · Department of Automation, Tsinghua University, Beijing 100084, China

Feature Attribution Neuro-Symbolic Reasoning Explainability Evaluation

Jul 2, 2026cs.AI

G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

In this work, we focus on SE-RRMs, a symbol-equivariant instantiation of RRMs that exhibits improved extrapolation to larger problem sizes. We propose a neuro-symbolic approach, ``Guiding with Recurrent Reasoning Models'' (G-RRM), which integrates SE-RRMs with symbolic solvers for constraint satisfaction problems. SE-RRMs act as neural solvers that generate full solution proposals and guide classical symbolic solvers, such as backtracking or SAT-based methods like Glucose 4.1 and CaDiCaL 3.0.0, that produce globally correct solutions. Centrally, we investigate when neural guidance with G-RRM improves the search efficiency of symbolic solvers. % Our experiments show that the efficacy of G-RRM depends on two conditions: first, the problem instances must have an expansive combinatorial search space to expose potential gains, and second, the solver architecture must be capable of dynamically overwriting its branching choices to recover when neural hints are imperfect. When these conditions hold, guidance drives median conflict counts to zero and yields significant wall-clock speedups: on

9\times9

Sudoku, where the SE-RRM correctly solves

91.1\%

of instances, backtracking accelerates by

33.3\times

and Glucose 4.1 by

1.70\times

(median,

p<0.001

), with Glucose 4.1 retaining a

1.17\times

speedup on perfect-hint

25\times25

grids. In contrast, CaDiCaL 3.0.0, whose runtime is overhead-dominated and which always respects the injected branching hints rather than overwriting them, shows no significant speedup (median

1.02\times

, n.s.) and even a small significant mean slowdown (

0.90\times

) on

9\times9

. These results delineate the regimes in which neural guidance translates into practical speedups.

Timo Bertram, Sidhant Bhavnani, Richard Freinschlag +3

ELLIS Unit Linz, LIT AI Lab & Institute for Machine Learning, Johannes Kepler University Linz, Austria · Institute for Symbolic Artificial Intelligence, Johannes Kepler University Linz, Austria · Clinical Research Institute for Medical AI, Johannes Kepler University Linz, Austria

Symbolic Reasoning Neuro-Symbolic Reasoning Constraint Satisfaction Inference-Time Guidance

Jul 2, 2026cs.RO

NEUROSYMLAND: Neuro-Symbolic Landing-Site Assessment for Robust and Edge-Deployable UAV Autonomy

Safe landing-site assessment in unstructured environments remains a key challenge for autonomous UAV deployment, as vision-only learning approaches often degrade under terrain variability and provide limited transparency in safety decisions. We present NEUROSYMLAND, a neuro-symbolic landing-site assessment system that integrates lightweight perception with explicit safety reasoning. The framework constructs a probabilistic semantic scene graph from onboard visual input and evaluates candidate landing regions using symbolic constraints capturing terrain flatness, obstacle clearance, and spatial consistency, enabling structured reasoning under perceptual uncertainty while maintaining edge-feasible execution. Across 72 simulated landing scenarios spanning diverse terrains, NEUROSYMLAND achieves 61 successful assessments, outperforming four competitive baselines (37-57 successes). To evaluate deployability, we further conduct 100 hardware-in-the-loop trials with randomized initial poses, profiling end-to-end latency, stage-wise execution time, and system-level metrics including CPU/GPU utilization, memory footprint, and power consumption. Results demonstrate improved robustness and interpretability with bounded edge-resource usage. Profiling shows that symbolic reasoning contributes only a small fraction of end-to-end latency, while the main computational cost arises from perception and PSSG construction. These results demonstrate the feasibility of deploying the landing-site assessment stack on edge-constrained UAV hardware, and all source code, datasets, prompts, and symbolic rule refinement examples are released in an open-source repository

Weixian Qian, Tianyi Yang, Sebastian Schroder +5

School of Computing, Macquarie University, Sydney, NSW, Australia. · Department of Computer Science, University of California, Santa Barbara, CA, USA. · Anitron

Aerial Robotics Neuro-Symbolic Reasoning Edge AI

Jul 1, 2026cs.AI

Graph-Native Reinforcement Learning Enables Traceable Scientific Hypothesis Generation through Conceptual Recombination

Accelerating materials discovery requires AI systems that can generate scientifically valid hypotheses through multi-step, domain-grounded reasoning. Standard large language models often produce fluent but weakly traceable responses to open-ended materials design problems, making it difficult to determine whether final answers are supported by coherent intermediate reasoning. We develop Graph-PRefLexOR, a family of graph-native reasoning models fine-tuned with Group Relative Policy Optimization (GRPO) to organize reasoning into explicit phases for mechanism exploration, graph construction, pattern extraction, and hypothesis synthesis. This design links neural language generation with symbolic relational structure, enabling causal connections to be constructed, inspected, and reused. On 100 open-ended questions from materials science and mechanics literature, Graph-PRefLexOR achieves 40-65% improvements over corresponding base models, with the largest gains in reasoning traceability. Embedding analyses show broader semantic exploration and approximately 2-3 times greater semantic diversity than baselines. Semantic backtracking and layer-wise hidden-state analyses further show stronger alignment between structured reasoning and final answers. Finally, test-time graph expansion reveals that additional compute primarily increases long-range conceptual recombination within a bounded semantic space, rather than simply expanding semantic coverage. These results establish graph-native reinforcement learning as a pathway toward interpretable AI systems for scientific hypothesis generation in materials design and other scientific applications.

Subhadeep Pal, Shashwat Sourav, Tirthankar Ghosal +1

Department of Civil and Environmental Engineering MASSACHUSETTS INSTITUTE OF TECHNOLOGY Cambridge, MA, USA · Department of Physics Washington University in St. Louis St. Louis, MO, USA · Computing and Computational Sciences Directorate Oak Ridge National Laboratory Oak Ridge, TN, USA +3

LLM Reasoning with Graphs RL for Language Model Reasoning Scientific Hypothesis Generation Materials Science Neuro-Symbolic Reasoning Large Language Model-Guided Scientific Discovery

Jun 30, 2026cs.AI

PolicyGuard: From Organizational Policies to Neuro-SymbolicCompliance Review Engines

Policy-grounded document review requires determining whether a target document complies with organization-specific policies, guidelines, or playbooks. While large language models can assist with policy interpretation and document analysis, end-to-end prompting leaves the applied policy logic implicit, making compliance decisions difficult to inspect, update, and test. We present PolicyGuard, a neuro-symbolic framework for policy-grounded document compliance review. PolicyGuard converts organizational policy guidance into an executable review engine consisting of typed relational logic rules and atom-level extraction questions. During review, LLMs answer these local questions using retrieved document evidence, and a symbolic evaluator applies the formal rules to detect non-compliance. We instantiate and evaluate PolicyGuard on company-specific NDA compliance review, where contract clauses must be checked against organization-specific negotiation policies. By separating policy formalization, local document interpretation, and symbolic compliance evaluation, PolicyGuard makes document review more explicit, maintainable, and systematically testable.

Sameer Malik, Ayush Singh, Amar Prakash Azad

1Fujitsu Research India Private Limited, Bengaluru, India

Legal Document Analysis Neuro-Symbolic Reasoning

Jun 26, 2026cs.AI

Verifiable Geometry Problem Solving: Solver-Driven Autoformalization and Theorem Proposing

Geometry Problem Solving have increasingly adopt the neuro-symbolic paradigm, combining neural intuition with symbolic rigor. However, current frameworks suffer from severe bottlenecks in two core stages: autoformalization, which treats multimodal translation as a static task decoupled from downstream solver compatibility, and theorem prediction, where solvers frequently hit a deductive impasse due to fixed rule libraries. To address these, we propose SD-GPS, a solver-driven framework that treats the symbolic solver as an execution oracle throughout both formalization and deduction. First, Solver-Driven Autoformalization unifies supervised formal-language adaptation and solvability-guided reinforcement learning into a single module built on QwenVL3-2B, making executability the central training signal. Second, Verified Theorem Proposing introduces an impasse-aware agent that proposes local auxiliary lemmas from current proof states, ensuring soundness by filtering all proposals through symbolic verification. Empirical evaluations on Geometry3K and PGPS9K demonstrate that SD-GPS consistently outperforms existing MLLM, neural, and neuro-symbolic methods across standard completion, multiple-choice, and cross-modal reference regimes, proving that closing the loop between multimodal perception and symbolic execution significantly improves geometric reasoning, offering profound insights into how neural agents can be grounded by formal systems to achieve verifiable problem-solving capabilities.

Can Li, Ting Zhang, Junbo Zhao +1

Beijing Normal University

Automated Theorem Proving Multimodal Reasoning Mathematical Reasoning Neuro-Symbolic Reasoning Autoformalization

Jun 24, 2026cs.AI

Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law

Sphere neural networks have achieved symbolic level syllogistic reasoning without training data, raising the question of where the limit of the scaling law for logical reasoning lies, i.e., whether data-driven machine learning systems can achieve the same level by increasing training data and training time. We show two methodological limitations that prevent supervised deep learning from reaching the symbolic-level syllogistic reasoning: (1) training data can not distinguish all 24 types of valid syllogistic reasoning; (2) end-to-end mapping from premises to conclusion introduces contradictory training targets between neural components for pattern recognition and logical reasoning. Beside theoretical analysis, we experimentally illustrate that Euler Net cannot achieve rigorous syllogistic reasoning. We further challenge the most recent ChatGPTs (GPT-5-nano and GPT-5) to determine the satisfiability of syllogistic statements in four surface forms (patterns): words, double words, simple symbols, and long random symbols, showing that surface forms affect the reasoning performance and that ChatGPT GPT-5 may reach 100% accuracy but still provide incorrect explanations. As empirical training processes are stopped after achieving 100% accuracy, we conclude that supervised machine learning systems will not attain the rigour of symbolic logical reasoning.

Tiansi Dong, Mateja Jamnik, Pietro Liò

The Alan Turing Institute, 96 Euston Road, London, NW1 2DB, UK. · Department of Computer Science and Technology, University of Cambridge, 15 JJ Thomson Ave., Cambridge, CB3 0FD, UK.

Logical Reasoning Symbolic Reasoning Scaling Laws Neuro-Symbolic Reasoning LLM Reasoning

Jun 22, 2026cs.AI

Neuro-Symbolic Drive: Rule-Grounded Faithful Reasoning for Driving VLAs

Driving VLA models incorporating Chain-of-Thought (CoT) reasoning are attractive because they leverage pretrained VLM representations and expose intermediate decisions in natural language, yet current rationales often lack the step-by-step decision semantics needed to keep the rationale causally connected to the planned motion. We introduce Neuro-Symbolic Drive, a neuro-symbolic driving framework that supervises a driving VLA with rule-grounded reasoning traces extracted directly from classical rule-based planners. Our key observation is that rule-based planners are symbolic AI systems that already function as executable reasoning engines: they reason about active safety constraints, search over candidate maneuvers, and select a final trajectory. We instrument these planners in simulation to capture both the executed trajectory and the internal decision trace at each rule-evaluation step. Each trace is serialized into structured rule-grounded reasoning and paired with the trajectory to fine-tune Qwen3.5-4B as a driving VLA. Because these traces are derived directly from the planner states that determine the action, they ensure reasoning is structurally coupled to motion generation by construction, rather than by post-hoc alignment. On our simulator-generated benchmark, detailed rule-grounded reasoning reduces ADE@3s from 0.47 to 0.26 and miss rate from 8.30% to 6.40% under three-camera perception, and from 0.54 to 0.26 and 10.13% to 5.99% under eight-camera perception. Neuro-Symbolic Drive thus converts neuro-symbolic planning logic into structured supervision. Code base: https://github.com/XiangboGaoBarry/Neural-Symbolic-Drive.

Xiangbo Gao, Xiukun Huang, Boyu Lu +5

1Texas A&M University · 2Carnegie Mellon University · University of Maryland +2

VLMs for Autonomous Driving Neuro-Symbolic Reasoning Autonomous Driving Planning