Recovering Explanations from Transformed Rule-Based Ontologies

Datalog rules are often used to define ontologies over Knowledge Graphs. Rule reasoners routinely optimise such ontologies by rewriting their rules into a form that can be evaluated more efficiently. These transformations preserve the entailed facts, but not the structure of the underlying derivations. A proof tree under the rewritten rules explains why a fact holds, but does not readily yield an explanation in terms of the original rules. We study the problem of constructing, from a proof of entailment under the rewritten rules, a proof under the original ones: we establish its computational complexity and identify two practically relevant languages for specifying proof transformations.

Tractable Query Answering under Epistemic Confidentiality Policies in DL Ontologies (extended version)

We study Controlled Query Evaluation (CQE), a declarative approach to confidentiality-preserving data access, in the context of Description Logic (DL) ontologies, and for confidentiality policies expressed through Epistemic Dependencies (EDs). We first address the problem of answering queries (specifically, Boolean unions of conjunctive queries) under known semantics for CQE (GA- and IGA-entailment). Our results show that if the TBox is expressed in $\text{DL-Lite}_{\mathcal{R}}$, CQE is computationally intractable in general. Moreover, in the presence of EDs, the IGA semantics has recently been proven not to satisfy an important confidentiality preservation property known as indistinguishability. With the goal of defining computationally easier and confidentiality-preserving forms of CQE, we introduce a new semantics for CQE, based on the notion of minimal policy violation (MPV). We show that the new semantics provides a sound approximation of the previous ones, while satisfying the indistinguishability property. We also prove that, in the case of $\text{DL-Lite}_{\mathcal{R}}$ ontologies, query entailment under the MPV semantics can be decided in polynomial time in data complexity. Finally, we present a software implementation of our framework that we used to evaluate the feasibility of this new approach using an existing benchmark for OWL 2 QL.

Fuzzy Quantification over OWL Ontologies and Knowledge Graphs

This paper presents a versatile framework for evaluating fuzzy quantification queries over both standard and fuzzy ontologies as well as knowledge graphs. The primary objective is the retrieval of individuals that satisfy queries articulated via Type I or Type II fuzzy quantified expressions. A key advantage of the proposed approach is its inherent adaptability: it remains 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). Furthermore, we present Q2S2, a publicly accessible implementation of this system developed to support future research.