Aus der Einleitung: „In this paper, we reuse the representation formalism `description graph' in order to characterize subsumption of ALN-concepts. The description logic ALN allows for conjunction, valuerestrictions, number restrictions, and primitive negation. Since Classic allows for more constructors than ALN, e.g., equality restrictions an attribute chains by the constructor SAME-AS,we can confine the notion of description graphs from [BP94]. On the other hand, ALN explicitly allows for primitive negation which yields another possibility { besides conflicting number restrictions { to express inconsistency. Thus, we have to modify the notion of canonical description graphs in order to cope with inconsistent concepts in the structural characterization of subsumption. It turns out that the description graphs obtained from ALN-concepts are in fact trees. A canonical graph is a deterministic tree. The conditions required by the structural characterization of subsumption on these trees can be tested by an eficient algorithm, i.e., we obtain an algorithm deciding subsumption of C and D in time polynomial in the size of C and D. The report is structured as follows. In the preliminaries, we define syntax and semantics of the description logic ALN as well as the inference problem of subsumption. In Section 3, we introduce description graphs, the data structure our structural subsumption algorithm is working on. Besides syntax and semantics also an algorithm for translating ALN-concepts into description graphs is given. Thereafter, we present the main result of this report in Section 6, a characterization of subsumption of ALN-concepts by a structural comparison of corresponding description graphs. Furthermore, a structural subsumption algorithm can be found in Section 6.2. In the last section we summarize our results and give an outlook to further applications of structural subsumption in terminological knowledge representation systems.

Aus der Einleitung: „Equational unification is a generalization of syntactic unification in which semantic properties of function symbols are taken into account. For example, assume that the function symbol '+' is known to be commutative. Given the unication problem x + y ≐ a + b (where x and y are variables, and a and b are constants), an algorithm for syntactic unification would return the substitution {x ↦ a; y ↦ b} as the only (and most general) unifier: to make x + y and a + b syntactically equal, one must replace the variable x by a and y by b. However, commutativity of '+' implies that {x ↦ b; y ↦ b} also is a unifier in the sense that the terms obtained by its application, namely b + a and a + b, are equal modulo commutativity of '+'. More generally, equational unification is concerned with the problem of how to make terms equal modulo a given equational theory, which specifies semantic properties of the function symbols that occur in the terms to be unified.”

Computing the least common subsumer (lcs) in description logics is an inference task first introduced for sublanguages of CLASSIC. Roughly speaking, the lcs of a set of concept descriptions is the most specific concept description that subsumes all of the input descriptions. As such, the lcs allows to extract the commonalities from given concept descriptions, a task essential for several applications like, e.g., inductive learning, information retrieval, or the bottom-up construction of KR-knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an lcs algorithm for the description logic ALEN, which allows for both constructors (as well as concept conjunction, primitive negation, and value restrictions). The proof of correctness of our lcs algorithm is based on an appropriate structural characterization of subsumption in ALEN also introduced in this paper. / This research was carried out while the second author was still at the LuFG Theoretical Computer Science, RWTH Aachen.

When trying to apply recently developed approaches for updating Description Logic ABoxes in the context of an action programming language, one encounters two problems. First, updates generate so-called Boolean ABoxes, which cannot be handled by traditional Description Logic reasoners. Second, iterated update operations result in very large Boolean ABoxes, which, however, contain a huge amount of redundant information. In this paper, we address both issues from a practical point of view.

Whereas matching in Description Logics is now relatively well investigated, there are only very few formal results on matching under additional side conditions, though these side conditions were already present in the original paper by Borgida and McGuinness introducing matching in DLs. The present report closes this gap for the DL ALN and its sublanguages.

In a previous report we have investigates subsumption in the presence of terminological cycles for the description logic EL, which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usually considered for cyclic definitions in description logics. This result depends on a characterization of subsumption through the existence of certain simulation relations on the graph associated with a terminology. In the present report we will use this characterization to show how the most specific concept and the least common subsumer can be computed in EL with cyclic definitions. In addition, we show that subsumption in EL (with or without cyclic definitions) remains polynomial even if one adds a certain restricted form of global role-value-maps to EL. In particular, this kind of role-value-maps can express transitivity of roles.

We investigate the impact that general concept inclusions and role-value maps have on the complexity and decidability of reasoning in the Description Logic FL₀. On the one hand, we give a more direct proof for ExpTimehardness of subsumption w.r.t. general concept inclusions in FL₀. On the other hand, we determine restrictions on role-value maps that ensure decidability of subsumption, but we also show undecidability for the cases where these restrictions are not satisfied.

Classical regular path queries (RPQs) can be too restrictive for some applications and answering such queries under approximate semantics to relax the query is desirable. While for answering regular path queries over graph databases under approximate semantics algorithms are available, such algorithms are scarce for the ontology-mediated setting. In this paper we extend an approach for answering RPQs over graph databases that uses weighted transducers to approximate paths from the query in two ways. The first extension is to answering approximate conjunctive 2-way regular path queries (C2RPQs) over graph databases and the second is to answering C2RPQs over ELH and DL-LiteR ontologies. We provide results on the computational complexity of the underlying reasoning problems and devise approximate query answering algorithms.

We adapt existing approaches for privacy-preserving publishing of linked data to a setting where the data are given as Description Logic (DL) ABoxes with possibly anonymised (formally: existentially quantified) individuals and the privacy policies are expressed using sets of concepts of the DL EL. We provide a chacterization of compliance of such ABoxes w.r.t. EL policies, and show how optimal compliant anonymisations of ABoxes that are noncompliant can be computed. This work extends previous work on privacypreserving ontology publishing, in which a very restricted form of ABoxes, called instance stores, had been considered, but restricts the attention to compliance. The approach developed here can easily be adapted to the problem of computing optimal repairs of quantified ABoxes. / This is an extended version of an article pulished in: Proceedings of the 19th International Semantic Web Conference (ISWC 2020), Springer LNCS

In recent work, we have shown how to compute compliant anonymizations of quantified ABoxes w.r.t. EL policies. In this setting, quantified ABoxes can be used to publish information about individuals, some of which are anonymized. The policy is given by concepts of the Description Logic (DL) EL, and compliance means that one cannot derive from the ABox that some non-anonymized individual is an instance of a policy concept. If one assumes that a possible attacker could have additional knowledge about some of the involved non-anonymized individuals, then compliance with a policy is not sufficient. One wants to ensure that the quantified ABox is safe in the sense that none of the secret instance information is revealed, even if the attacker has additional compliant knowledge. In the present paper, we show that safety can be decided in polynomial time, and that the unique optimal safe anonymization of a non-safe quantified ABox can be computed in exponential time, provided that the policy consists of a single EL concept. / This is an extended version of an article published in: Proceedings of the 36th ACM/SIGAPP Symposium on Applied Computing (SAC ’21), ACM