Large Language Models (LLMs) have demonstrated remarkable proficiency in natural language understanding, yet they struggle with strict multi-step reasoning, frequently suffering from hallucinations and inconsistency. Existing solutions like Chain-of-Thought (CoT) lack rigorous verification mechanisms, while standard Retrieval-Augmented Generation (RAG) often misses the complex, structural dependencies inherent in logical tasks. To bridge this gap, we propose a Neuro-Symbolic architecture that integrates a Logical Knowledge Graph (LKG) with dynamic solver routing. Specifically, we introduce an ontology-based LKG that treats logical rules and constraints as first-class topological nodes, enabling explicit modeling of dependencies extracted from text. We further design a Logic Router to dynamically dispatch tasks to the optimal symbolic engine, which is supported by a topology-aware hybrid retrieval mechanism. Experimental results on logical reasoning benchmarks demonstrate that our framework significantly outperforms state-of-the-art prompting and RAG baselines, delivering higher accuracy and verifiable reasoning paths.
Institutional policies stay in natural language while the systems that check compliance demand machine-readable constraints. Bridging that gap is still done by hand. PolicyKG closes the loop. It is an LLM pipeline that reads a policy PDF, classifies each sentence as an obligation, permission, or prohibition, lifts the label into first-order deontic logic, and emits SHACL constraints. Four stages run on a LangGraph state machine with per-stage validators. The piece that matters most is the Corpus Adapter: a YAML vocabulary registry that grounds LLM predicates in a target ontology. Retargeting to a new domain means swapping the registry, not retraining a model. On the Asian Institute of Technology Policies and Procedures corpus (1,663 sentences, 443 rules), PolicyKG reaches 86.9% deontic classification accuracy (Cohen's kappa = .709). Three annotators independently re-label a 50-item sample and agree at Fleiss' kappa = .844. SHACL shape correctness on a 69-shape subset is F1 = .866. The FOL path handles 79.2% of rules; the rest go through a direct NL-to-SHACL fallback. We audited every one of the 443 rules for second- or higher-order constructs. An automated regex checklist flagged none, and a first-author pass on the 92 FOL-fallback cases confirmed the same. The exact upper 95% Clopper-Pearson bound on the true HOL rate is 0.67%. This is an audit finding for one corpus, not a proof of FOL sufficiency for institutional policy. Swapping the AIT registry for a GDPR registry raises exact property alignment from 1/15 to 11/15 (Fisher's exact p < .001; Cohen's h = 1.53). On the LexDeMod lease-contract benchmark (N = 200), Macro F1 drops to .370 because lease English uses "shall be entitled" for permission -- exactly the vocabulary mismatch registry swap is meant to fix. Repeated runs produce hash-identical SHACL outputs.
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.