We investigate semiring provenance--a successful framework originally defined in the relational database setting--for description logics. In this context, the ontology axioms are annotated with elements of a commutative semiring and these annotations are propagated to the ontology consequences in a way that reflects how they are derived. We define a provenance semantics for a language that encompasses several lightweight description logics and show its relationships with semantics that have been defined for ontologies annotated with a specific kind of annotation (such as fuzzy degrees). We show that under some restrictions on the semiring, the semantics satisfies desirable properties (such as extending the semiring provenance defined for databases). We then focus on the well-known why-provenance, which allows to compute the semiring provenance for every additively and multiplicatively idempotent commutative semiring, and for which we study the complexity of problems related to the provenance of an axiom or a conjunctive query answer. Finally, we consider two more restricted cases which correspond to the so-called positive Boolean provenance and lineage in the database setting. For these cases, we exhibit relationships with well-known notions related to explanations in description logics and complete our complexity analysis. As a side contribution, we provide conditions on an ELHI_bot ontology that guarantee tractable reasoning.

Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens and which provides explicit operators for the abstraction and refinement of concepts and roles across multiple abstraction levels, based on conjunctive queries. We prove that reasoning in the resulting family of DLs is decidable while several seemingly harmless variations turn out to be undecidable. We also pinpoint the precise complexity of our logics and several relevant fragments.

There is a niche of companies responsible for intermediating the purchase of large batches of varied products for other companies, for which the main challenge is to perform product description standardization, i.e., matching an item described by a client with a product described in a catalog. The problem is complex since the client's product description may be: (1) potentially noisy; (2) short and uninformative (e.g., missing information about model and size); and (3) cross-language. In this paper, we formalize this problem as a ranking task: given an initial client product specification (query), return the most appropriate standardized descriptions (response). In this paper, we propose TPDR, a two-step Transformer-based Product and Class Description Retrieval method that is able to explore the semantic correspondence between IS and SD, by exploiting attention mechanisms and contrastive learning. First, TPDR employs the transformers as two encoders sharing the embedding vector space: one for encoding the IS and another for the SD, in which corresponding pairs (IS, SD) must be close in the vector space. Closeness is further enforced by a contrastive learning mechanism leveraging a specialized loss function. TPDR also exploits a (second) re-ranking step based on syntactic features that are very important for the exact matching (model, dimension) of certain products that may have been neglected by the transformers. To evaluate our proposal, we consider 11 datasets from a real company, covering different application contexts. Our solution was able to retrieve the correct standardized product before the 5th ranking position in 71% of the cases and its correct category in the first position in 80% of the situations. Moreover, the effectiveness gains over purely syntactic or semantic baselines reach up to 3.7 times, solving cases that none of the approaches in isolation can do by themselves.

Knowledge graphs (KGs) have emerged as a prominent data representation and management paradigm. Being usually underpinned by a schema (e.g. an ontology), KGs capture not only factual information but also contextual knowledge. In some tasks, a few KGs established themselves as standard benchmarks. However, recent works outline that relying on a limited collection of datasets is not sufficient to assess the generalization capability of an approach. In some data-sensitive fields such as education or medicine, access to public datasets is even more limited. To remedy the aforementioned issues, we release PyGraft, a Python-based tool that generates highly customized, domain-agnostic schemas and knowledge graphs. The synthesized schemas encompass various RDFS and OWL constructs, while the synthesized KGs emulate the characteristics and scale of real-world KGs. Logical consistency of the generated resources is ultimately ensured by running a description logic (DL) reasoner. By providing a way of generating both a schema and KG in a single pipeline, PyGraft's aim is to empower the generation of a more diverse array of KGs for benchmarking novel approaches in areas such as graph-based machine learning (ML), or more generally KG processing. In graph-based ML in particular, this should foster a more holistic evaluation of model performance and generalization capability, thereby going beyond the limited collection of available benchmarks. PyGraft is available at: https://github.com/nicolas-hbt/pygraft.

The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable extensions outside first-order logic. We introduce universally quantified concepts, which take the form of variables that can be replaced with arbitrary concepts, and define two semantics of this extension. A schema semantics allows replacements of concept variables only by concepts from a particular language, giving us axiom schemata similar to modal logics. A second-order semantics allows replacement of concept variables with arbitrary subsets of the domain, which is similar to quantified predicates in second-order logic. To study the proposed semantics, we focus on the extension of the description logic $\mathcal{EL}$. We show that for a useful fragment of the extension, the conclusions entailed by the different semantics coincide, allowing us to use classical $\mathcal{EL}$ reasoning algorithms even for the second-order semantics. For a slightly smaller, but still useful, fragment, we were also able to show polynomial decidability of the extension. This fragment, in particular, can express a generalized form of role chain axioms, positive self restrictions, and some forms of (local) role-value-maps from KL-ONE, without requiring any additional constructors.

Description logic (DL) ontologies extend knowledge graphs (KGs) with conceptual information and logical background knowledge. In recent years, there has been growing interest in inductive reasoning techniques for such ontologies, which promise to complement classical deductive reasoning algorithms. Similar to KG completion, several existing approaches learn ontology embeddings in a latent space, while additionally ensuring that they faithfully capture the logical semantics of the underlying DL. However, they suffer from several shortcomings, mainly due to a limiting role representation. We propose Box$^2$EL, which represents both concepts and roles as boxes (i.e., axis-aligned hyperrectangles) and demonstrate how it overcomes the limitations of previous methods. We theoretically prove the soundness of our model and conduct an extensive experimental evaluation, achieving state-of-the-art results across a variety of datasets. As part of our evaluation, we introduce a novel benchmark for subsumption prediction involving both atomic and complex concepts.

Ontologies are used in various domains, with RDF and OWL being prominent standards for ontology development. RDF is favored for its simplicity and flexibility, while OWL enables detailed domain knowledge representation. However, as ontologies grow larger and more expressive, reasoning complexity increases, and traditional reasoners struggle to perform efficiently. Despite optimization efforts, scalability remains an issue. Additionally, advancements in automated knowledge base construction have created large and expressive ontologies that are often noisy and inconsistent, posing further challenges for conventional reasoners. To address these challenges, researchers have explored neuro-symbolic approaches that combine neural networks' learning capabilities with symbolic systems' reasoning abilities. In this chapter,we provide an overview of the existing literature in the field of neuro-symbolic deductive reasoning supported by RDF(S), the description logics EL and ALC, and OWL 2 RL, discussing the techniques employed, the tasks they address, and other relevant efforts in this area.

Answering temporal CQs over temporalized Description Logic knowledge bases (TKB) is a main technique to realize ontology-based situation recognition. In case the collected data in such a knowledge base is inaccurate, important query answers can be missed. In this paper we introduce the TKB Alignment problem, which computes a variant of the TKB that minimally changes the TKB, but entails the given temporal CQ and is in that sense (cost-)optimal. We investigate this problem for ALC TKBs and conjunctive queries with LTL operators and devise a solution technique to compute (cost-optimal) alignments of TKBs that extends techniques for the alignment problem for propositional LTL over finite traces.

We investigate the impact of non-regular path expressions on the decidability of satisfiability checking and querying in description logics extending ALC. Our primary objects of interest are ALCreg and ALCvpl, the extensions of with path expressions employing, respectively, regular and visibly-pushdown languages. The first one, ALCreg, is a notational variant of the well-known Propositional Dynamic Logic of Fischer and Ladner. The second one, ALCvpl, was introduced and investigated by Loding and Serre in 2007. The logic ALCvpl generalises many known decidable non-regular extensions of ALCreg. We provide a series of undecidability results. First, we show that decidability of the concept satisfiability problem for ALCvpl is lost upon adding the seemingly innocent Self operator. Second, we establish undecidability for the concept satisfiability problem for ALCvpl extended with nominals. Interestingly, our undecidability proof relies only on one single non-regular (visibly-pushdown) language, namely on r#s# := { r^n s^n | n in N } for fixed role names r and s. Finally, in contrast to the classical database setting, we establish undecidability of query entailment for queries involving non-regular atoms from r#s#, already in the case of ALC-TBoxes.

The necessity to manage inconsistency in Description Logics Knowledge Bases (KBs) has come to the fore with the increasing importance gained by the Semantic Web, where information comes from different sources that constantly change their content and may contain contradictory descriptions when considered either alone or together. Classical reasoning algorithms do not handle inconsistent KBs, forcing the debugging of the KB in order to remove the inconsistency. In this paper, we exploit an existing probabilistic semantics called DISPONTE to overcome this problem and allow queries also in case of inconsistent KBs. We implemented our approach in the reasoners TRILL and BUNDLE and empirically tested the validity of our proposal. Moreover, we formally compare the presented approach to that of the repair semantics, one of the most established semantics when considering DL reasoning tasks.