Fuzzy Quantification over OWL Ontologies and Knowledge Graphs

LLMs have revolutionized knowledge representation and retrieval, but lack the explicit modeling that knowledge ontologies possess. This paper surveys the ways that ontologies and knowledge graphs have been integrated with dense embedding algorithms. All hitherto attempts involve a trade-off between probabilistic and crisp inference. This paper proposes a novel frontier for devising knowledge representation systems that can simultaneously accommodate probabilistic and crisp inference in the same representation. To this effect, the paper proposes neuro-quantum-fuzzy systems as knowledge representation systems that accommodate both classical and contextual inference implemented through quantum-neural networks (QNN).

Query optimization of Basic Graph Patterns (BGP) SPARQL queries over Knowledge Graphs (KG) requires accurate cardinality estimation. Recently published learned estimators outperform statistics- and sampling-based approaches, but share a limitation preventing their adoption in real-world triplestores: they are transductive and require retraining when the underlying graph changes or when applied to new graphs. We present FICE (Fully Inductive Cardinality Estimation), the first learned cardinality estimator for BGP queries over KGs that generalizes to entirely unseen graphs (including unseen relations), without any retraining. FICE is a graph neural network (GNN) with two coupled components. First, an encoder GNN over a factor-graph view of the KG produces entity and relation embeddings. We prove that BGP cardinality is a local function of the 2-hop neighborhood around bound terms in this view, motivating the local message-passing encoder. A decoder GNN then composes these embeddings along the join topology of the query to predict log-cardinality. The encoder and decoder are trained jointly, making the embeddings specialized for cardinality estimation. FICE is trained using neighborhood sampling to scale to KGs with millions of triples, and decouples embedding generation from cardinality decoding to enable estimation latency below a millisecond. Compared to learned and non-learned baselines over 10 KGs, FICE reduces the overall median q-error from 13.54 (for the best competitor) to 5.34 and dominates all approaches in tail behavior.

Natural language interfaces to databases have gained popularity, yet the theoretical foundations for evaluating and designing these systems remain underdeveloped. We present QUEST (Query Understanding Evaluation through Semantic Translation), a framework resting on two independently motivated components: the FAR structural invariant, which holds that every well-formed query reduces to Filter, Aggregate, and Return operations; and the W5H dimensional framework, which holds that all filtering criteria map to six semantic dimensions (Who, What, Where, When, Why, and How). Validated across five text-to-SQL datasets (n = 120,464), FAR conformance is universal across all domains and schema types, while W5H dimensional profiles vary substantially. Healthcare queries are strongly concentrated in temporal (WHEN: 80.4%) and person-centric (WHO: 73.0%) dimensions far exceeding general-domain benchmarks, and causal (WHY) and mechanistic (HOW) reasoning are near-zero everywhere, with apparent HOW exceptions reflecting quantitative aggregation rather than genuine procedural reasoning. These results identify a frontier that must be crossed for genuine machine reasoning over structured data.