Fuzzy Quantification over OWL Ontologies: paper and Q2S2 release

Fuzzy Quantification over OWL Ontologies and Knowledge Graphs, a paper by Enrique Palacín, Fernando Bobillo, Ignacio Huitzil, Francesca A. Lisi and Umberto Straccia, was submitted to arXiv on 24 Jun 2026 as arXiv:2606.25778 (https://doi.org/10.48550/arXiv.2606.25778). The paper introduces a versatile framework for evaluating fuzzy quantification queries and ships Q2S2, a publicly accessible implementation developed to support future research.

What does the paper introduce?

The paper introduces a framework that evaluates fuzzy quantification queries over both standard and fuzzy ontologies as well as RDFS knowledge graphs, targeting retrieval of individuals that satisfy Type I or Type II fuzzy quantified expressions. The approach is explicitly agnostic to the quantifier type, the underlying evaluation method, and the specific ontology data source, meaning it is intended to work with OWL ontologies and RDFS knowledge graphs without embedding hard assumptions about quantifiers or evaluation algorithms.

The abstract states the primary objective is the retrieval of individuals satisfying queries articulated via Type I or Type II fuzzy quantified expressions. The submission notes the framework's adaptability as a key advantage and records a public implementation named Q2S2 for future research use.

How does the system handle different quantifiers and data sources?

The framework treats the quantifier type, the evaluation method and the ontology data source as orthogonal concerns, so it can operate across OWL ontologies and RDFS knowledge graphs without changing the core query semantics. That agnosticism allows the same query formulation to be evaluated whether the input is a standard ontology, a fuzzy ontology, or a knowledge graph.

The paper frames this design choice as central: being "entirely agnostic to the quantifier type, the underlying evaluation method, and the specific data source of the ontology (i.e., OWL ontologies or RDFS knowledge graphs)." This lets researchers swap quantifier definitions or evaluation strategies without reworking the query layer.

How can researchers use Q2S2?

Q2S2 is provided as a publicly accessible implementation intended to support follow-up work, experiments and comparisons across quantifiers and evaluation methods. The authors present Q2S2 alongside the framework to facilitate experimentation with the paper's ideas.

The arXiv entry highlights Q2S2 as a deliverable developed "to support future research." That implies immediate availability for replication, benchmarking and integration with existing ontology and knowledge graph tooling.

Why it matters

Fuzzy quantification sits at the intersection of ontology reasoning and approximate querying. A framework that separates quantifier choice, evaluation method and data source reduces the engineering friction in testing alternative fuzzy quantifiers on real ontologies and knowledge graphs. Making an implementation available, Q2S2, increases the chance that new quantifier designs can be evaluated head-to-head on the same inputs, which should speed comparative work and reproducibility in this niche.

The paper also broadens the applicability of fuzzy querying: by covering both OWL ontologies and RDFS knowledge graphs, the approach invites work that crosses the traditional divide between semantic web and knowledge graph communities.

What to watch

Watch for the DataCite DOI registration that arXiv notes as pending, and for follow-up papers or code forks that adopt Q2S2. A concrete signal of uptake will be subsequent research that reuses Q2S2 to compare Type I and Type II quantifiers on shared datasets or that cites arXiv:2606.25778 in empirical evaluations.