Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. First, our TKRS is equipped with a highly expressive concept, language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, it allows one to express inclusion statements between general concepts, in particular to express terminological cycles. We provide a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases based on the general technique of constraint systems.

Description logics are a family of knowledge representation formalisms that are descended from semantic networks and frames via the system Kl-one. During the last decade, it has been shown that the important reasoning problems (like subsumption and satisfiability) in a great variety of description logics can be decided using tableau-like algorithms. This is not very surprising since description logics have turned out to be closely related to propositional modal logics and logics of programs (such as propositional dynamic logic), for which tableau procedures have been quite successful. Nevertheless, due to different underlying intuitions and applications, most description logics differ significantly from run-of-the-mill modal and program logics. Consequently, the research on tableau algorithms in description logics led to new techniques and results, which are, however, also of interest for modal logicians. In this article, we will focus on three features that play an important role in description logics (number restrictions, terminological axioms, and role constructors), and show how they can be taken into account by tableau algorithms.

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove co-NP-completeness. 1

One of the main characteristics of knowledge representation systems based on the description of concepts is the clear distinction between terminological and assertional knowledge. Although this characteristic leads to several computational and representational advantages, it usually limits the expressive power of the system. For this reason, some attempts have been done, allowing for a limited form of amalgamation between the two components and a more complex interaction between them. In particular, one of these attempts is based on letting the individuals to be referenced in the concept expressions. This is generally performed by admitting a constructor for building a concept from a set of enumerated individuals. In this paper we investigate on the consequences of introducing constructors of this type in the concept description language. We also provide a complete reasoning procedure to deal with these constructors and we obtain some complexity results on it. 1 Introduction The ide...

The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting is NP-complete; the data-complexity of both query-answering and finite query-answering for the two-variable guarded fragment with counting is co-NP-complete.

Conjunctive queries (CQ) are fundamental for accessing description logic (DL) knowledge bases. We study CQ answering in (extensions of) the DL EL, which is popular for large-scale ontologies and underlies the designated OWL2-EL profile of OWL2. Our main contribution is a novel approach to CQ answering that enables the use of standard relational database systems as the basis for query execution. We evaluate our approach using the IBM DB2 system, with encouraging results. 1

The novel context of accessing and querying large data repositories through ontologies that are formalized in terms of expressive DLs requires on the one hand to consider query answering as the primary inference technique, and on the other hand to optimize it with respect to the size of the data, which dominates the size of ontologies. While the complexity of DLs has been studied extensively, data complexity in expressive DLs has been characterized only for answering atomic queries, and was still open for more expressive query languages, such as unions of conjunctive queries (UCQs). In this paper we advocate the need for studying this problem, and provide a significant technical contribution in this direction. Specifically, we prove a tight coNP upper bound for answering UCQs over SHIQ knowledge bases, for the case where the queries do not contain transitive roles. We thus establish that for a whole range of DLs from AL to SHIQ, answering such UCQs has coNP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, inspired by the one in [20], but which manages the technical challenges of simultaneous inverse roles and number restrictions (which leads to a DL lacking the finite model property). 1

Traditionally, the core of a Terminological Knowledge Representation System (TKRS) consists of a TBox or terminology, where concepts are introduced, and an ABoxorworld description, where facts about individuals are stated in terms of concept memberships. This design has a drawback because in most applications the TBox has to meet two functions at a time: On the one hand---similarly to a database schema---frame-like structures with type information are introduced through primitive concepts and primitive roles; on the other hand, views on the objects in the knowledge base are provided through defined concepts. We propose to account for this conceptual separation by partitioning the TBox into two components for primitive and defined concepts, whichwe call the schema and the view part. We envision the two parts to differ with respect to the language for concepts, the statements allowed, and the semantics. We argue that this separation achieves more conceptual clarity about the role of primit...

Conjunctive query answering is an important DL reasoning task. Although this task is by now quite well-understood, tight complexity bounds for conjunctive query answering in expressive DLs have never been obtained: all known algorithms run in deterministic double exponential time, but the existing lower bound is only an EXPTIME one. In this paper, we prove that conjunctive query answering in ALCI is 2-EXPTIME-hard (and thus complete), and that it becomes NEXPTIME-complete under some reasonable assumptions.

Traditionally, the core of a Terminological Knowledge Representation System (TKRS) consists of a so-called TBox, where concepts are introduced, and an ABox, where facts about individuals are stated in terms of these concepts. This design has a drawback because in most applications the TBox has to meet two functions at a time: on the one hand, similar to a database schema, framelike structures with typing information are introduced through primitive concepts and primitive roles; on the other hand, views on the objects in the knowledge base are provided through defined concepts. We propose to account for this conceptual separation by partitioning the TBox into two components for primitive and defined concepts, which we call the schema and the view part. We envision the two parts to differ with respect to the language for concepts, the statements allowed, and the semantics. We argue that by this separation we achieve more conceptual clarity about the role of primitive and defined concep...