Recently, it has been shown that the small DL EL, which allows for conjunction and existential restrictions, has better algorithmic properties than its counterpart FL₀, which allows for conjunction and value restrictions. Whereas the subsumption problem in FL₀ becomes already intractable in the presence of aclyc TBoxes, it remains tractable in EL even w.r.t. general concept inclusion axioms (GCIs). On the one hand, we will extend the positive result for EL by identifying a set of expressive means that can be added to EL without sacrificing tractability. On the other hand, we will show that basically all other additions of typical DL constructors to EL with GCIs make subsumption intractable, and in most cases even EXPTIME-complete. In addition, we will show that subsumption in FL₀ with GCIs is EXPTIME-complete.

The tableau algorithm implemented in the FaCT knowledge representation system decides satisfiability and subsumption in SHIQ, a very expressive description logic providing, e.g., inverse and transitive roles, number restrictions, and general axioms. Intuitively, the algorithm searches for a tree-shaped abstraction of a model. To ensure termination of this algorithm without comprimising correctness, it stops expanding paths in the search tree using a so-called 'double-blocking' condition.

We call a Herbrand model of a set of first-order clauses finite, if each of the predicates in the clauses is interpreted by a finite set of ground terms. We consider first-order clauses with the signature restricted to unary predicate and function symbols and one variable. Deciding the existence of a finite Herbrand model for a set of such clauses is known to be ExpTime-hard even when clauses are restricted to an anti-Horn form. Here we present an ExpTime algorithm to decide if a finite Herbrand model exists in the more general case of arbitrary clauses. Moreover, we describe a way to generate finite Herbrand models, if they exist. Since there can be infinitely many minimal finite Herbrand models, we propose a new notion of acyclic Herbrand models. If there is a finite Herbrand model for a set of restricted clauses, then there are finitely many (at most triple-exponentially many) acyclic Herbrand models. We show how to generate all of them.

Unification in the Description Logic (DL) FL₀ is known to be ExpTimecomplete, and of unification type zero. We investigate in this paper whether a lower complexity of the unification problem can be achieved by either syntactically restricting the role depth of concepts or semantically restricting the length of role paths in interpretations. We show that the answer to this question depends on whether the number formulating such a restriction is encoded in unary or binary: for unary coding, the complexity drops from ExpTime to PSpace. As an auxiliary result, which is however also of interest in its own right, we prove a PSpace-completeness result for a depth-restricted version of the intersection emptiness problem for deterministic root-to-frontier tree automata. Finally, we show that the unification type of FL₀ improves from type zero to unitary (finitary) for unification without (with) constants in the restricted setting.

Description Logics (DLs) [BCM+07] are prominent modeling formalisms underlying the Web Ontology Language (OWL). The lightweight DL EL in particular is used to formulate many biomedical ontologies. DLs allow to represent subconcept-superconcept relationships between concepts, e.g., diseases, as well as more complex correspondences. Unification in DLs has been proposed as a non-standard reasoning task to detect redundant concepts in ontologies [BN01, BM10b]. Recently, disunification in EL has been investigated and several algorithms were proposed to solve disunification problems [BBM16].

Golog programs allow to model complex behaviour of agents by combining primitive actions defined in a Situation Calculus theory using imperative and non-deterministic programming language constructs. In general, verifying temporal properties of Golog programs is undecidable. One way to establish decidability is to restrict the logic used by the program to a Description Logic (DL), for which recently some complexity upper bounds for verification problem have been established. However, so far it was open whether these results are tight, and lightweight DLs such as EL have not been studied at all. Furthermore, these results only apply to a setting where actions do not consume time, and the properties to be verified only refer to the timeline in a qualitative way. In a lot of applications, this is an unrealistic assumption. In this work, we study the verification problem for timed Golog programs, in which actions can be assigned differing durations, and temporal properties are specified in a metric branching time logic. This allows to annotate temporal properties with time intervals over which they are evaluated, to specify for example that some property should hold for at least n time units, or should become specified within some specified time window. We establish tight complexity bounds of the verification problem for both expressive and lightweight DLs. Our lower bounds already apply to a very limited fragment of the verification problem, and close open complexity bounds for the non-metrical cases studied before.

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic EL to disunification since negative constraints on unifiers can be used to avoid unwanted unifiers. While decidability of the solvability of general EL-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we restrict the attention to solutions that are built from so-called atoms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of (general) disunification problems.

Unification in description logics (DLs) has been introduced as a novel inference service that can be used to detect redundancies in ontologies, by finding different concepts that may potentially stand for the same intuitive notion. It was first investigated in detail for the DL FL₀, where unification can be reduced to solving certain language equations. In order to increase the recall of this method for finding redundancies, we introduce and investigate the notion of approximate unification, which basically finds pairs of concepts that “almost” unify. The meaning of “almost” is formalized using distance measures between concepts. We show that approximate unification in FL₀ can be reduced to approximately solving language equations, and devise algorithms for solving the latter problem for two particular distance measures.

Recently introduced approaches for relaxed query answering, approximately defining concepts, and approximately solving unification problems in Description Logics have in common that they are based on the use of concept comparison measures together with a threshold construction. In this paper, we will briefly review these approaches, and then show how weighted automata working on infinite trees can be used to construct computable concept comparison measures for FL₀ that are equivalence invariant w.r.t. general TBoxes. This is a first step towards employing such measures in the mentioned approximation approaches. / Accepted to LATA 2017

Snomed CT is a widely used medical ontology which is formally expressed in a fragment of the Description Logic EL++. The underlying logics allow for expressive querying, yet make it costly to maintain and extend the ontology. Existing approaches for ontology generation mostly focus on learning superclass or subclass relations and therefore fail to be used to generate Snomed CT definitions. In this paper, we present an approach for the extraction of Snomed CT definitions from natural language texts, based on the distance relation extraction approach. By benefiting from a relatively large amount of textual data for the medical domain and the rich content of Snomed CT, such an approach comes with the benefit that no manually labelled corpus is required. We also show that the type information for Snomed CT concept is an important feature to be examined for such a system. We test and evaluate the approach using two types of texts. Experimental results show that the proposed approach is promising to assist Snomed CT development.