Symbolic Reasoning

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6 papers in the last four weeks, up 50% on the four weeks before. 0.1% of all new papers.

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Latest papers 55

Jun 12, 2026cs.LG

EM-NeSy: Expectation Maximization for Neurosymbolic Learning

Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.

Annegret Seibt, Luc De Raedt, Giuseppe Marra

Department of Computer Science KU Leuven

Symbolic Reasoning Expectation-Maximization Neuro-Symbolic Reasoning Neurosymbolic Learning

Jun 8, 2026cs.CL

SEF-CLGC at SemEval-2026 Task 11: Logical Notation Impact on Language Model Performance

This paper revisits our pipeline called Syllogistic Evaluation Framework-Common Logic Grammar Construction (SEF-CLGC). We combine formal logical notations with Small Language Models (SLMs) to evaluate reasoning performance on the SemEval-2026 Task 11 Subtask 1: Disentangling Content and Formal Reasoning in Large Language Models. Our experiments show that by relying solely on SLMs, trained on a combination of natural and symbolic languages, our best model achieves a content score of 27.80% on the task while significantly lowering the content bias in reasoning.

Hanna Abi Akl, Fabien Gandon, Catherine Faron +1

Université Côte d’Azur, Inria, CNRS, I3S, Sophia Antipolis, France · Data ScienceTech Institute, Paris, France

Logical Reasoning Symbolic Reasoning Language Model Bias Evaluation LLM Reasoning

Jun 7, 2026cs.AI

Artificial Intelligence for Mathematical Reasoning: An Integrated Survey of Language Models, Neuro-symbolic Systems, and Verified Discovery

Mathematical reasoning has long served as a stringent test of machine intelligence; over the past decade, it has moved from a niche problem within NLP to one of the most consequential AI frontiers. This survey provides a unified account of the field's evolution, from early rule-based math word problem (MWP) solvers and template-driven geometry systems, through neural expression generation and LLM prompting, to contemporary reasoning models, multi-agent systems, neuro-symbolic theorem provers, and verified discovery workflows. We organize the landscape along four axes: (i) informal reasoning over text and diagrams, spanning MWP solving, multimodal geometry, and VLMs; (ii) formal reasoning in proof assistants, including autoformalization, tactic prediction, compiler-guided repair, and proof search; (iii) mathematical discovery, where systems propose constructions, improve bounds, or assist attacks on open problems; and (iv) the inference and training-time techniques, including CoT prompting, tool use, process reward models, and RLVR, that increasingly connect generation with verification. We catalog major benchmarks across grade-school arithmetic, competition mathematics, geometry, formal proving, multimodal and multilingual reasoning, and expert evaluation, and we examine benchmark saturation, contamination, reporting mismatches, and the distinction between pass@1, majority voting, and verifier-assisted pass@

k

. We critically assess failure modes: brittleness under perturbation, reward hacking, multimodal grounding failures, fragile formalization, and the energy cost of reasoning-scale inference. Drawing on recent perspectives from working mathematicians, we identify future directions centered on verified-discovery workflows, reasoning efficiency, and infrastructure to make AI-assisted formalization broadly usable. Companion materials: https://github.com/Starscream-11813/awesome-AI4Math.

Syed Rifat Raiyan, Mohsinul Kabir, Hasan Mahmud +2

Systems and Software Lab (SSL), Department of Computer Science and Engineering, Islamic University of Technology, Gazipur, Bangladesh · Department of Computer Science, University of Manchester, Manchester, United Kingdom

Mathematical Reasoning Benchmarks Automated Theorem Proving Symbolic Reasoning Mathematical Reasoning Neuro-Symbolic Reasoning LLM Mathematical Reasoning

Jun 3, 2026cs.CL

Imbuing Large Language Models with Bidirectional Logic for Robust Chain Repair

Autoregressive chain-of-thought (CoT) reasoning in large language models (LLMs) is fundamentally forward-directed: each step conditions only on prior tokens. This unidirectional inductive bias renders even capable models susceptible to error snowballing, wherein a single logical or arithmetic mistake in an early step irreversibly corrupts the entire reasoning chain. We introduce Teleological Reasoning Infilling (\TRI{}), a training framework that endows decoder-only transformers with a native \emph{goal-conditioned bridging} capability. The key insight is to reframe erroneous reasoning segments as fill-in-the-middle (FIM) tasks: given a verified prefix premise

P

, a verified downstream milestone

S

, and the original query

Q

, the model must synthesise the logical bridge

M

that connects

P

to

S

rigorously and completely. To achieve this with standard causal architectures, we introduce a Prefix-Suffix-Middle (PSM) sequence rearrangement with three non-overlapping sentinel tokens, enabling

M

to attend to both

P

and

S

without any structural modification to the self-attention mechanism. Training proceeds in two stages: (i) Supervised Fine-Tuning (SFT) on symbolically verified

(P, S, M)

triples extracted from formal mathematics corpora, and (ii) Direct Preference Optimisation (DPO) with a deterministic symbolic verifier (Lean 4 / Python) as the sole reward oracle, eliminating LLM-judge sycophancy. At inference, TRI operates as a surgical repair module within a dual-system loop: a causal draft model generates an initial trace, the verifier pinpoints failures, and TRI infills only the damaged segment, leaving verified sections intact. Comprehensive experiments on three benchmarks demonstrate that TRI achieves state-of-the-art performance across all tasks, while reducing per-problem token expenditure by 31.2%.

Zehua Cheng, Wei Dai, Jiahao Sun +1

Department of Computer Science, University of Oxford, UK · Institute of Logic and Computation, TU Wien, Austria

LLM Self-Correction Symbolic Reasoning Mathematical Reasoning Structured Reasoning LLM Reliability Efficient Language Model Inference+1

Jun 2, 2026cs.AI

AUDITFLOW: Executable Symbolic Environments for Structured Financial Reporting Verification

Structured financial audit verification is difficult for language-model agents because correctness depends on structured evidence rather than text alone. A model must link reported facts to taxonomy concepts, traverse calculation or dimensional relations, and recompute expected values before applying an audit rule. We propose AuditFlow, a graph-grounded multi-agent framework that separates adaptive search from deterministic verification. AuditFlow builds a symbolic environment from a static US-GAAP taxonomy graph and a dynamic XBRL filing graph, and exposes it through typed tools for fact retrieval, taxonomy traversal, numerical checking, and rule evaluation. Two junior auditors inspect each case from regulatory and evidentiary views, while a senior auditor resolves disagreements and can request further investigation. The final reports are fused through evidential aggregation to produce an audit verdict, expected value, evidence trail, and trustworthiness score. On a FinAuditing-derived FinMR sample, AuditFlow reaches 82.09% joint audit accuracy under GPT-5.5, outperforming the strongest baseline by 14.93 points. Removing deterministic checks drops accuracy to 17.91%, showing that the symbolic environment performs the verification step that the model cannot reliably replace.

Yan Wang, Xuguang Ai, Jaisal Patel +7

The Fin AI, USA · Rensselaer Polytechnic Institute, USA · Université de Montréal, Canada +3

Symbolic Reasoning Multi-Agent Systems Finance

May 30, 2026cs.AI

AXIOM: A Trust-First Neuro-Symbolic Execution Architecture for Verifiable Mathematical Reasoning

We present AXIOM, a trust-first neuro-symbolic execution architecture for natural-language mathematical reasoning. In AXIOM, the language model functions strictly as a canonicalizer: it rewrites informal problem text into a narrow schema consumed by a deterministic Computer-Algebra-System (CAS) pipeline, which derives and verifies the answer or abstains as a first-class output. Routing follows a 1:1:1 alignment between problem-shape regex, schema-specific prompt, and closed-form CAS handler, with 3,100+ such routes shipped and zero LOST_CORRECT regressions across 250+ consecutive ship commits. We report empirical results on 4 MATH categories with a cumulative correctness of 94.36% (2,592/2,747) at 100.00% trust on parseable (zero confident-wrong answers across the full 2,747-record benchmark), all four domains above the per-domain 70/90/70 floor with per-domain trust at 100.0%, and median latency of 1 ms on rule-only handlers (88% of records on the lm-eval arithmetic 20,000-record benchmark). The architecture has served ~30,000 production queries through a public deployment. The contribution we emphasize is not a final accuracy figure but the forward dynamic the architecture establishes: every logged abstain in production is a candidate correct after one ship cycle, since new tasks compose without regressing the registry. The operational discipline behind this property -- math-template bucketing, LOST_CORRECT scan as regression oracle, parseable-first onboarding, and abstain as first-class output -- constitutes a transferable framework for trustworthy neuro-symbolic systems beyond mathematics.

Alessio Bruno

Independent researcher

LLM Answer Verification Symbolic Reasoning Neuro-Symbolic Reasoning LLM Mathematical Reasoning

May 29, 2026cs.AI

MAVEN: Improving Generalization in Agentic Tool Calling

Generalization across agentic tool-calling environments remains a central challenge for reliable agentic reasoning systems. Although large language models achieve strong results on individual benchmarks, their ability to compose reasoning strategies, preserve intermediate states, and coordinate tools across domains remains underexplored. We present MAVEN (Modular Agentic Verification and Execution Network), a lightweight symbolic reasoning scaffold for structured decomposition, adaptive tool orchestration, and intermediate verification. We evaluate MAVEN across established tool-calling benchmarks, including BFCL v3, TauBench, Tau2Bench, AceBench, and introduce MAVEN-Bench, a stress-test benchmark for multi-step mathematical and physical reasoning with explicit verification and adversarial task composition. MAVEN-Bench exposes a substantial gap between partial reasoning quality and end-to-end task success; in direct MAVEN-Bench runs, MAVEN improves its GPT-OSS-120b base model from 48% to 71% accuracy without additional training. It also remains competitive with frontier proprietary baselines while using an open-weight backbone with an estimated cost ratio of roughly 1/10, suggesting that lightweight verification-centered scaffolds can strengthen compositional reasoning and motivate more process-aware evaluation of agents in the wild.

Omkar Ghugarkar, Vishvesh Bhat, Muhammad Ahmed Mohsin +1

CoreThink AI, USA · Stanford University, Stanford, CA, USA

Logical Reasoning LLM Agent Evaluation Symbolic Reasoning AI Agent Benchmarks Agentic Reasoning LLM Tool Use+1

May 11, 2026cs.CV

Hilbert-Geo: Solving Solid Geometric Problems by Neural-Symbolic Reasoning

Geometric problem solving, as a typical multimodal reasoning problem, has attracted much attention and made great progress recently, however most of works focus on plane geometry while usually fail in solid geometry due to 3D spatial diagrams and complex reasoning. To bridge this gap, we introduce Hilbert-Geo, the first unified formal language framework for solid geometry, including an extensive predicate library and a dedicated theorem bank. Based on this framework, we propose a Parse2Reason method containing two steps of first parsing then reasoning. In the parsing step, we utilize conditional description language (CDL), a formalized language composed of predicates specifically designed to construct geometric conditions, to represent both problem description (natural text) and solid diagrams (visual image). In the reasoning step, we leverage those formal CDL and the theorem bank to perform relational inference and algebraic computation, generating strictly correct, verifiable, and human-readable reasoning processes. Notably, our proposed Hilbert-Geo is also applicable to plane geometry. To advance geometric reasoning, we curate two expert-annotated dataset SolidFGeo2k and PlaneFGeo3k, which are furnished with geometric formal language annotations, solutions and answers. Extensive experiments show that our proposed method achieves the state-of-the-art (SOTA) performance 77.3% in SolidFGeo2k and 84.1% in MathVerse-Solid (one small subset in MathVerse dedicated to solid geometry), substantially outperforming leading MLLMs, such as Gemini-2.5-pro (54.2% on SolidFGeo2k) and GPT-5 (62.9% on MathVerse-Solid). In addition, our method achieves the SOTA accuracy 80.2% in PlaneFGeo3k, demonstrating the generality of the Hilbert-Geo in geometric reasoning. Our code and datasets are released at https://github.com/PremiLab-Math/Hilbert-Geo.

Ruoran Xu, Haoyu Cheng, Bin Dong +1

Xi’an Jiaotong-Liverpool University · Ricoh Software Research Center Beijing Co.,Ltd.

Symbolic Reasoning Multimodal Reasoning Mathematical Reasoning Neuro-Symbolic Reasoning

May 9, 2026cs.AI

DiagnosticIQ: A Benchmark for LLM-Based Industrial Maintenance Action Recommendation from Symbolic Rules

Monitoring complex industrial assets relies on engineer-authored symbolic rules that trigger based on sensor conditions and prompt technicians to perform corrective actions. The bottleneck is not detection but response: translating rules into maintenance steps requires asset-specific knowledge gained through years of practice. We investigate whether LLMs can serve as decision support for this rule-to-action step and introduce \ours{}, a benchmark of 6{,}690 expert-validated multiple-choice questions from 118 rule-action pairs across 16 asset types. We contribute (i) a symbolic-to-MCQA pipeline normalizing rules to Disjunctive Normal Form with embedding-based distractor sampling, (ii) five variants probing distinct failure modes (Pro, Pert, Verbose, Aug, Rationale), and (iii) a benchmark of 29 LLMs and 4 embedding baselines. A human evaluation (9 practitioners, mean 45.0%) confirms \ours{} requires specialist knowledge beyond operational experience. Three findings stand out. The frontier has closed: the top three LLMs lie within one Macro point, with Bradley-Terry Elo placing claude-opus-4-6 30 points above the next model. Yet \ours{},Pro exposes brittleness, with every model losing 13--60% relative accuracy under distractor expansion. \ours{},Aug exposes pattern-matching: under condition inversion, frontier models still select the original answer 49--63% of the time. The deployment bottleneck is not capability but calibration: frontier models handle template-style fault detection but break under structural perturbation.

Devin Yasith De Silva, Dhaval Patel, Christodoulos Constantinides +7

2Rensselaer Polytechnic Institute · 1IBM · 3Independent Contributor

Logical Reasoning LLM Evaluation Predictive Maintenance Symbolic Reasoning Language Model Robustness

May 6, 2026cs.CL

ReaComp: Compiling LLM Reasoning into Symbolic Solvers for Efficient Program Synthesis

LLMs can solve program synthesis tasks but remain inefficient and unreliable on hard instances requiring large combinatorial search. Given a small set of reasoning traces, we use coding agents to compile them into reusable symbolic program synthesizers over constrained DSLs. The resulting solvers require no LLM calls at test time and are strong standalone systems: symbolic solver ensembles reach 91.3% accuracy on PBEBench-Lite and 84.7% on PBEBench-Hard, outperforming LLMs with test-time scaling for the latter by +16.3 percentage points at zero LLM inference cost. They also complement LLM search, improving PBEBench-Hard accuracy from 68.4% to 85.8% while reducing reported token usage by 78%, and raising SLR-Bench hard-tier accuracy from 34.4% to 58.0% in a neuro-symbolic hybrid setting. Compared to directly using coding agents as per-instance solvers, induced solvers are substantially more Pareto-efficient, amortizing a small one-time construction cost over many zero-token executions. Finally, most solvers transfer zero-shot to a real historical linguistics task - predicting sound changes in natural language data - reaching 80.1% accuracy under ensembling and recovering some plausible linguistic rules. Together, these results show that reasoning traces can be compiled into reusable symbolic solvers that solve many tasks directly, complement LLM inference on hard cases, and provide a scalable route to domain-general solver induction. We release code and data for reproducibility.

Atharva Naik, Yash Mathur, Prakam +2

Carnegie Mellon University · Independent Researcher

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

May 6, 2026cs.CL

UFAL-CUNI at SemEval-2026 Task 11: An Efficient Modular Neuro-symbolic Method for Syllogistic Reasoning

This paper describes our system submitted to SemEval-2026 Task 11: Disentangling Content and Formal Reasoning in Large Language Models. We present an efficient modular neuro-symbolic approach, combining a symbolic prover with small reasoning LLMs (4B parameters). The system consists of an LLM-based parser that translates natural language syllogisms to a first-order logic (FOL) representation, an automated theorem prover, and two optional modules: machine translation for multilingual inputs and a symbolic retrieval component for the identification of relevant premises. The system achieves competitive accuracy and relatively low content effect on most subtasks. Our ablations show that this approach outperforms LLM-based zero-shot baselines in this parameter size range, but also reveal limited multilingual capabilities of small LLMs. Finally, we include a discussion of the task's main ranking metric and analyze its limitations.

Ivan Kartáč, Kristýna Onderková, Jan Bronec +3

Institute of Formal and Applied Linguistics, Faculty of Mathematics and Physics, Charles University

Logical Reasoning Symbolic Reasoning Neuro-Symbolic Reasoning

Apr 30, 2026cs.AI

Language Models Refine Mechanical Linkage Designs Through Symbolic Reflection and Modular Optimisation

Designing mechanical linkages involves combinatorial topology selection and continuous parameter fitting. We show that language models can systematically improve linkage designs through symbolic representations. Language model agents explore discrete topologies while numerical optimisers fit continuous parameters. A symbolic lifting operator translates simulator trajectories into qualitative descriptors, motion labels, temporal predicates, and structural diagnostics that models interpret across iterative design cycles. Across six engineering-relevant motion targets and three open-source models (Llama 3.3 70B, Qwen3 4B, Qwen3 MoE 30B-A3B), the modular architecture reduces geometric error by up to 68% and improves structural validity by up to 134% over monolithic baselines. Critically, 78.6% of iterative refinement trajectories show measurable improvement, with the system correctly diagnosing overconstraint (56.3%) and underconstraint (35.6%) failure modes and proposing grounded corrections. Models across all three families acquire interpretable mechanical reasoning strategies without fine-tuning, demonstrating that principled symbolic abstraction bridges generative AI and the numerical precision required for engineering design.

João Pedro Gandarela, Thiago Rios, Stefan Menzel +1

Idiap Research Institute, Switzerland · École Polytechnique Fédérale de Lausanne (EPFL), Switzerland · Honda Research Institute Europe, Germany +2

Mechanism Design Large Language Model-Guided Optimization Symbolic Reasoning

Apr 29, 2026cs.RO

LLM-Flax : Generalizable Robotic Task Planning via Neuro-Symbolic Approaches with Large Language Models

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.

Seongmin Kim, Daegyu Lee

Department of Physical AI Engineering, Jeonbuk National University(JBNU) · Faculty of Department of Advanced Defense Technology and Industry, Jeonbuk National University(JBNU)

Large Language Model-Based Robot Planning Symbolic Planning Symbolic Reasoning Robot Task Planning Neuro-Symbolic Reasoning

Apr 25, 2026cs.AI

Constraint-Based Analysis of Reasoning Shortcuts in Neurosymbolic Learning

Neurosymbolic systems can satisfy logical constraints during learning without achieving the intended concept-label correspondence; this is a problem known as reasoning shortcuts. We formalize reasoning shortcuts as a constraint satisfaction problem and investigate under which conditions concept mappings are uniquely determined by the constraints. We prove that a discrimination property (requiring that no valid concept mapping can be transformed into another valid mapping by swapping two concept values) is necessary for shortcut-freeness under bijective mappings, but demonstrate via a counterexample that it is insufficient even when the constraint graph is connected. We develop an ASP-based algorithm that verifies whether a given constraint set uniquely determines the intended concept mapping, with proven soundness and completeness. When shortcuts are detected, a greedy repair algorithm eliminates them by augmenting the constraint set, converging in at most

k

iterations, where

k

is the number of alternative valid mappings. We further provide a complexity classification: deciding shortcut-freeness is coNP-complete, counting shortcuts is #P-complete, and finding minimal repairs is NP-hard. We also establish sample complexity bounds showing that logarithmically many label queries suffice for disambiguation in favorable cases, while querying all ambiguous positions suffices in the worst case. Experiments across eight benchmark domains validate our approach.

Akihiro Takemura, Katsumi Inoue, Masaaki Nishino

National Institute of Informatics, Tokyo, Japan · Communication Science Laboratories, NTT, Inc., Japan

Symbolic Reasoning Constraint Satisfaction Neurosymbolic Learning

Apr 23, 2026cs.AI

To See the Unseen: on the Generalization Ability of Transformers in Symbolic Reasoning

We investigate the ability of decoder-only transformer models to perform abstract symbolic reasoning; specifically solving propositional logic reasoning problems given in-context. Previous work demonstrated that models fail to generalize to problems involving variable names that were not observed during training, and it was shown that one reason behind this is the difficulty of copying (or generating) unseen tokens. We show both theoretically and empirically that a particular representational collapse also has a crucial role: the unembeddings (last-layer weights) of unseen tokens collapse to nearly the same vector during training. The collapse makes distinguishing multiple unseen variables difficult for the model (especially when the embedding and unembedding parameters are shared), and provides a mechanistic explanation for the effectiveness of existing heuristic interventions like "active forgetting", which periodically reset the token (un)embeddings. Based on these observations, we devise a combination of techniques, involving a small architecture change facilitating copying, data diversity, and freezing or resetting (un)embeddings, that achieves generalization to unseen tokens. We support our claims with extensive controlled experiments on propositional logic reasoning problems. Beyond synthetic experiments, we also observe evidence of (un)embedding collapse in the open-weight models in the Gemma 3 family, which includes 99 unused tokens reserved for downstream use. Empirically we find that the correlated embeddings of these tokens are a poor initialization for finetuning applications.

Nevena Lazić, Liam Fowl, András György +1

Logical Reasoning Decoder-Only Language Models Symbolic Reasoning Compositional Generalization LLM Reasoning

Apr 23, 2026cs.AI

Symbolic Grounding Reveals Representational Bottlenecks in Abstract Visual Reasoning

Vision--language models (VLMs) often fail on abstract visual reasoning benchmarks such as Bongard problems, raising the question of whether the main bottleneck lies in reasoning or representation. We study this on Bongard-LOGO, a synthetic benchmark of abstract concept learning with ground-truth generative programs, by comparing end-to-end VLMs on raw images with large language models (LLMs) given symbolic inputs derived from those images. Using symbolic inputs as a diagnostic probe rather than a practical multimodal architecture, our \emph{Componential--Grammatical (C--G)} paradigm reformulates Bongard-LOGO as a symbolic reasoning task based on LOGO-style action programs or structured descriptions. LLMs achieve large and consistent gains, reaching mid--90s accuracy on Free-form problems, while a strong visual baseline remains near chance under matched task definitions. Ablations on input format, explicit concept prompts, and minimal visual grounding show that these factors matter much less than the shift from pixels to symbolic structure. These results identify representation as a key bottleneck in abstract visual reasoning and show how symbolic input can serve as a controlled diagnostic upper bound.

Mohit Vaishnav, Tanel Tammet

Applied Artificial Intelligence Group, Tallinn University of Technology, Estonia 12169 · Kimova AI, Tallinn, Estonia 10113

Logical Reasoning Visual Reasoning Symbolic Reasoning VLM Reasoning

Apr 22, 2026stat.ML

Efficient Symbolic Computations for Identifying Causal Effects

Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.

Benjamin Hollering, Pratik Misra, Nils Sturma

Max Planck Institute for Mathematics in the Sciences, Germany · Binghamton University, USA · École Polytechnique Fédérale de Lausanne, Switzerland

Structural Causal Models Symbolic Reasoning Causal Identifiability

Apr 21, 2026cs.CL

Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views

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.

Feihao Fang, My T. Thai, Yuanyuan Lei

University of Illinois Urbana-Champaign, Champaign, IL · Computer & Information Science and Engineering, University of Florida, Gainesville, FL

Symbolic Reasoning Neuro-Symbolic Reasoning Activation Steering LLM Reasoning

Apr 20, 2026cs.AI

From Natural Language to Executable Narsese: A Neuro-Symbolic Benchmark and Pipeline for Reasoning with NARS

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.

Mina Gabriel, Pei Wang

Temple University, Philadelphia, PA 19122, USA

Logical Reasoning Reasoning Evaluation Symbolic Reasoning Neuro-Symbolic Reasoning

Apr 20, 2026cs.CL

FregeLogic at SemEval 2026 Task 11: A Hybrid Neuro-Symbolic Architecture for Content-Robust Syllogistic Validity Prediction

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.

Adewale Akinfaderin, Nafi Diallo

Amazon Web Services Seattle, WA

Logical Reasoning Symbolic Reasoning Neuro-Symbolic Reasoning

Apr 19, 2026cs.AI

Recurrent Reasoning on Symbolic Puzzles with Sequence Models

Large language models often appear strong on symbolic and algorithmic tasks, yet this apparent strength can hide brittle behaviour when problems become longer, harder, or slightly out of distribution. A major limitation of current reasoning benchmarks is that many primarily test whether a model can produce a valid answer, while paying less attention to whether the solution is minimal, robust, and stable under controlled difficulty scaling. We introduce RecurrReason, a difficulty-controlled benchmark of four recurrent logic puzzles (Tower of Hanoi, River Crossing, Block World, and Checkers Jumping) with BFS-optimal trajectories and a single interpretable difficulty parameter

N \in \{1,\dots,10\}

, totalling 10{,}817 unique puzzles and 285{,}933 moves. We benchmark two Transformer families, an encoder-decoder model (T5-style) and a decoder-only model (GPT-2-style), under consistent data splits and evaluation criteria, training on

N{=}1

to

7

and evaluating on both held-out in-distribution instances and harder out-of-distribution instances at

N{=}8

to

10

. Fine-tuned pre-trained T5 achieves 97.27% validation and 81.00% OOD accuracy on Block World; all models score 0.00% on River Crossing under all conditions. Failure mode analysis reveals that architecture is a stronger determinant of success than scale. Pre-training transfers only to puzzles with locally structured transition functions. Our code and dataset will be open-sourced upon acceptance.

Gowrav Mannem, Chowdhury Marzia Mahjabin, Jason Chen +2

Algoverse AI Research · Cornell University

Symbolic Planning Symbolic Reasoning Language Model Robustness Algorithmic Reasoning

Apr 17, 2026cs.AI

Structured Abductive-Deductive-Inductive Reasoning for LLMs via Algebraic Invariants

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.

Sankalp Gilda, Shlok Gilda

DeepThought Solutions · Department of Computer Science · University of Florida

Logical Reasoning Abductive Reasoning Symbolic Reasoning Structured Reasoning Neuro-Symbolic Reasoning LLM Reasoning

Feb 11, 2026cs.CL

Neuro-Symbolic Synergy for World Modeling

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules--particularly in corner cases--is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM contributes candidate-level scores through log-linear reranking, without requiring the LLM to interpret rule text. Rule-guided sampling prioritizes transitions that are weakly covered by symbolic rules, using 35--60% of the training pairs while outperforming full-data supervised fine-tuning in five of six settings. Experiments on ScienceWorld, WebShop, and PlanCraft demonstrate consistent gains in WM prediction accuracy and data efficiency; one-step lookahead on open-ended WebShop also improves agent reward. Our models, rules, and code are available at https://github.com/tianyi-lab/NeSyS.

Hongyu Zhao, Siyu Zhou, Haolin Yang +2

Department of Computer Science University of Maryland College Park, MD 20742, USA · Faculty of Engineering and IT Australian AI Institute University of Technology Sydney Sydney, Australia · Department of Statistics University of Chicago Chicago, IL 60637, USA +2

LLM World Models World Model Learning World Models Symbolic Reasoning Neuro-Symbolic Reasoning

Jan 5, 2026hep-th

Machine learning modularity

Based on a transformer based sequence-to-sequence architecture combined with a dynamic batching algorithm, this work introduces a machine learning framework for automatically simplifying complex expressions involving multiple elliptic Gamma functions, including the

q

-

θ

function and the elliptic Gamma function. The model learns to apply algebraic identities, particularly the SL

(2,\mathbb{Z})

and SL

(3,\mathbb{Z})

modular transformations, to reduce heavily scrambled expressions to their canonical forms. Experimental results show that the model achieves over 99% accuracy on in-distribution tests and maintains robust performance (exceeding 90% accuracy) under significant extrapolation, such as with deeper scrambling depths. This demonstrates that the model has internalized the underlying algebraic rules of modular transformations rather than merely memorizing training patterns. Our work presents the first successful application of machine learning to perform symbolic simplification using modular identities, offering a new automated tool for computations with special functions in quantum field theory and the string theory.

Yi Fan, Vishnu Jejjala, Yang Lei

School of Physical Science and Technology, Soochow University, 333 Ganjiang Road, Suzhou 215006, P.R. China · Institute for Advanced Study, Soochow University, 333 Ganjiang Road, Suzhou 215006, P.R. China · Mandelstam Institute for Theoretical Physics, School of Physics and NITheCS, University of the Witwatersrand, Johannesburg 2050, South Africa +1

Symbolic Reasoning

Dec 8, 2025cs.CL

Training Language Models to Use Prolog as a Tool

Language models frequently produce plausible yet incorrect reasoning traces that are difficult to verify. We investigate fine-tuning models to use Prolog as an external symbolic reasoning tool, training Qwen2.5-3B-Instruct with Group Relative Policy Optimization (GRPO) on a cleaned version of GSM8K (which we release as gsm8k-prolog-prover). We systematically vary prompt structure, reward composition (execution, syntax, semantics, structure), and inference protocol (single-try, multiple-try, and two agentic modes). Our reinforcement learning approach outperforms supervised fine-tuning on GSM8K, and the resulting 3B model achieves zero-shot performance on MMLU-STEM and MMLU-Pro competitive with 7B few-shot baselines. Most importantly, we identify an accuracy--auditability trade-off: configurations tuned for correctness alone learn to delegate reasoning to natural language and use Prolog only for the final computation, while configurations rewarded for symbolic structure produce fully auditable programs at a cost in accuracy. We interpret this trade-off as a form of reward hacking and discuss its implications for deploying neurosymbolic systems in safety-critical domains. The source code for our experiments is available under https://github.com/aisilab/Prolog-as-a-Tool

Niklas Mellgren, Peter Schneider-Kamp, Lukas Galke Poech

University of Southern Denmark

Reward Hacking Logical Reasoning RL for Language Model Reasoning Symbolic Reasoning LLM Tool Use