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.

To ensure completeness Description Logics (DLs) are popular languages for knowledge of the method, the so-called refinement step is used that recomputes representation and reasoning. They are the underlying the abstraction based on new (sound) entailments formalism for the standardized Web Ontology Language obtained from a previous abstraction. This has the added OWL, which is widely used in many application areas. Recent benefit that not only consistency but also the full materialization years have also seen an increasing interest in ontologybased of the ABox can be computed without (rather expensive) data access, where a TBox with background knowledge, explanation computations or repeated consistency often expressed in a DL language, is used to enrich checks. This paper significantly advances the abstraction refinement datasets (ABoxes), which are then accessible via queries.

The paper presents an approach for optimizing the evaluation of SPARQL queries over OWL ontologies using SPARQL's OWL Direct Semantics entailment regime. The approach is based on the computation of lower and upper bounds, but we allow for much more expressive queries than related approaches. In order to optimize the evaluation of possible query answers in the upper but not in the lower bound, we present a query extension approach that uses schema knowledge from the queried ontology to extend the query with additional parts. We show that the resulting query is equivalent to the original one and we use the additional parts that are simple to evaluate for restricting the bounds of subqueries of the initial query. In an empirical evaluation we show that the proposed query extension approach can lead to a significant decrease in the query execution time of up to four orders of magnitude.

Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive interpretations such as "It is true at no fewer than 15 accessible worlds that...", or "It is true at no more than 2 accessible worlds that...". We investigate the complexity of satisfiability for this language over some familiar classes of frames. This problem is more challenging than its ordinary modal logic counterpart--especially in the case of transitive frames, where graded modal logic lacks the tree-model property. We obtain tight complexity bounds for the problem of determining the satisfiability of a given graded modal logic formula over the classes of frames characterized by any combination of reflexivity, seriality, symmetry, transitivity and the Euclidean property.