We investigate Controlled Query Evaluation (CQE) over ontologies, where information disclosure is regulated by epistemic dependencies (EDs), a family of logical rules recently proposed for the CQE framework. In particular, we combine EDs with the notion of optimal GA censors, i.e. maximal sets of ground atoms that are entailed by the ontology and can be safely revealed. We focus on answering Boolean unions of conjunctive queries (BUCQs) with respect to the intersection of all optimal GA censors - an approach that has been shown in other contexts to ensure strong security guarantees with favorable computational behavior. First, we characterize the security of this intersection-based approach and identify a class of EDs (namely, full EDs) for which it remains safe. Then, for a subclass of EDs and for DL-Lite_R ontologies, we show that answering BUCQs in the above CQE semantics is in AC^0 in data complexity by presenting a suitable, detailed first-order rewriting algorithm. Finally, we report on experiments conducted in two different evaluation scenarios, showing the practical feasibility of our rewriting function.

In Knowledge Graphs (KGs), where the schema of the data is usually defined by particular ontologies, reasoning is a necessity to perform a range of tasks, such as retrieval of information, question answering, and the derivation of new knowledge. However, information to populate KGs is often extracted (semi-) automatically from natural language resources, or by integrating datasets that follow different semantic schemas, resulting in KG inconsistency. This, however, hinders the process of reasoning. In this survey, we focus on how to perform reasoning on inconsistent KGs, by analyzing the state of the art towards three complementary directions: a) the detection of the parts of the KG that cause the inconsistency, b) the fixing of an inconsistent KG to render it consistent, and c) the inconsistency-tolerant reasoning. We discuss existing work from a range of relevant fields focusing on how, and in which cases they are related to the above directions. We also highlight persisting challenges and future directions.

The quality of ontologies and their alignments is crucial for developing high-quality semantics-based applications. Traditional debugging techniques repair ontology networks by removing unwanted axioms and mappings, but may thereby remove consequences that are correct in the domain of the ontology network. In this paper we propose a framework for repairing ontology networks that deals with this issue. It defines basic operations such as debugging, weakening and completing. Further, it defines combination operators that reflect choices in how and when to use the basic operators, as well as choices regarding the autonomy level of the ontologies and alignments in the ontology network. We show the influence of the combination operators on the quality of the repaired network and present an implemented tool. By using our framework together with existing algorithms for debugging, weakening and completing, we essentially provide a blueprint for extending previous work and systems.

-- Drug sample comparison is a process used by the French National Police to identify drug distribution networks. The current approach is based on a manual comparison done by forensic experts. In this article, we present our approach to acquire, formalise, and specify expert knowledge to improve the current process. We use an ontology coupled with logical rules to model the underlying knowledge. The different steps of our approach are designed to be reused in other application domains. The results obtained are explainable making them usable by experts in different fields. The fight against drug trafficking has been one of the French government's priorities since the end of 2019 and has led to the creation of the National Stup plan. This plan comprises 55 measures, including the use of new indicators to understand consumer habits and dealers' methods. The work described in this article is part of this plan and aims to support scientific experts in the decision-making process for narcotic profiling. As part of the fight against drug trafficking, several arrests may be made, often accompanied by seizures. Forensic experts perform several analyses on samples from a seizure. They aim to correlate different samples from different seizures to identify trafficking networks best. To do so, experts use sample matching to pair samples according to their characteristics. Paired samples constitute an ensemble called a batch. The sample characteristics used are represented by different data, namely: macroscopic data (e.g., sample dimension, drug logos), qualitative data (e.g., list of active substances), quantitative data (e.g., dosage of substances) or non-confidential seizure data (e.g., date, place of seizure). In France, such data is stored in the national STUPS database.

This paper is concerned with knowledge graph embedding with background knowledge, taking the formal perspective of logics. In knowledge graph embedding, knowledge— expressed as a set of triples of the form (a R b) (“a is R-related to b”)—is embedded into a real-valued vector space. The embedding helps exploiting geometrical regularities of the space in order to tackle typical inductive tasks of machine learning such as link prediction. Recent embedding approaches also consider incorporating background knowledge, in which the intended meanings of the symbols a, R, b are further constrained via axioms of a theory. Of particular interest are theories expressed in a formal language with a neat semantics and a good balance between expressivity and feasibility. In that case, the knowledge graph together with the background can be considered to be an ontology. This paper develops a cone-based theory for embedding in order to advance the expressivity of the ontology: it works (at least) with ontologies expressed in the description logic ALC, which comprises restricted existential and universal quantifiers, as well as concept negation and concept disjunction. In order to align the classical Tarskian Style semantics for ALC with the sub-symbolic representation of triples, we use the notion of a geometric model of an ALC ontology and show, as one of our main results, that an ALC ontology is satisfiable in the classical sense iff it is satisfiable by a geometric model based on cones. The geometric model, if treated as a partial model, can even be chosen to be faithful, i.e., to reflect all and only the knowledge captured by the ontology. We introduce the class of axis-aligned cones and show that modulo simple geometric operations any distributive logic (such as ALC) interpreted over cones employs this class of cones. Cones are also attractive from a machine learning perspective on knowledge graph embeddings since they give rise to applying conic optimization techniques.

The quality of ontologies in terms of their correctness and completeness is crucial for developing high-quality ontology-based applications. Traditional debugging techniques repair ontologies by removing unwanted axioms, but may thereby remove consequences that are correct in the domain of the ontology. In this paper we propose an interactive approach to mitigate this for $\mathcal{EL}$ ontologies by axiom weakening and completing. We present algorithms for weakening and completing and present the first approach for repairing that takes into account removing, weakening and completing. We show different combination strategies, discuss the influence on the final ontologies and show experimental results. We show that previous work has only considered special cases and that there is a trade-off between the amount of validation work for a domain expert and the quality of the ontology in terms of correctness and completeness.

We focus on handling conflicting and uncertain information in lightweight ontologies, where uncertainty is represented in a possibilistic logic setting. We use DL-Lite, a tractable fragment of Description Logic, to specify terminological knowledge (i.e., TBox). We assume the TBox to be stable and coherent, while its combination with a set of assertional facts (i.e., ABox) may be inconsistent. We address the problem of dealing with conflicts when the reliability relation between sources is only partially ordered. We propose to represent the uncertain ABox as a symbolic weighted base, where a strict partial preorder is applied on the weights.

Recently, various methods for representation learning on Knowledge Bases (KBs) have been developed. However, these approaches either only focus on learning the embeddings of the data-level knowledge (ABox) or exhibit inherent limitations when dealing with the concept-level knowledge (TBox), e.g., not properly modelling the structure of the logical knowledge. We present BoxEL, a geometric KB embedding approach that allows for better capturing logical structure expressed in the theories of Description Logic EL++. BoxEL models concepts in a KB as axis-parallel boxes exhibiting the advantage of intersectional closure, entities as points inside boxes, and relations between concepts/entities as affine transformations. We show theoretical guarantees (soundness) of BoxEL for preserving logical structure. Namely, the trained model of BoxEL embedding with loss 0 is a (logical) model of the KB. Experimental results on subsumption reasoning and a real-world application--protein-protein prediction show that BoxEL outperforms traditional knowledge graph embedding methods as well as state-of-the-art EL++ embedding approaches.

We propose an approach based on Answer Set Programming for reasoning about actions with domain descriptions including ontological knowledge, expressed in the lightweight description logic EL^\bot. We consider a temporal action theory, which allows for non-deterministic actions and causal rules to deal with ramifications, and whose extensions are defined by temporal answer sets. We provide conditions under which action consistency can be guaranteed with respect to an ontology, by a polynomial encoding of an action theory extended with an EL^\bot knowledge base (in normal form) into a temporal action theory.

The W3C Web Ontology Language (OWL) is a powerful knowledge representation formalism at the basis of many semantic-centric applications. Since its unrestricted usage makes reasoning undecidable already in case of very simple tasks, expressive yet decidable fragments have been identified. Among them, we focus on OWL 2 RL, which offers a rich variety of semantic constructors, apart from supporting all RDFS datatypes. Although popular Web resources - such as DBpedia - fall in OWL 2 RL, only a few systems have been designed and implemented for this fragment. None of them, however, fully satisfy all the following desiderata: (i) being freely available and regularly maintained; (ii) supporting query answering and SPARQL queries; (iii) properly applying the sameAs property without adopting the unique name assumption; (iv) dealing with concrete datatypes. To fill the gap, we present DaRLing, a freely available Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries. In particular, we describe its architecture, the rewriting strategies it implements, and the result of an experimental evaluation that demonstrates its practical applicability. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).