Abstract: The more DLs are being used in applications such as the Semantic Web [2], biology, and the clinical sciences, the more certain expressive weaknesses are commented upon. A recurring set of these comments is due to the fact that only few DLs and even fewer DL reasoners support forms of defeasible reasoning. For example, Rector describes in [12, 16] how useful statements such as “the heart of a human is normally located on the left hand side of the body” could be for the clinical sciences, and OWL design patterns have been developed to work around the lack of such statements. Various combinations of DLs with nonmonotonic formalisms have been investigated so far. DL-MKNF, the combination of DLs with minimal knowledge and negation as failure (MKNF) [9] is introduced in [4]. DL-MKNF extends DLs with two modal operators and is considered to be a unified framework for nonmonotonic extensions of DLs since various nonmonotonic logics can be embedded into MKNF [9]; these include default logic [13] and autoepistemic logic [10]. The combination of DLs with default logic was introduced [1], implemented in Pellet [7], and its translation into DL-MKNF was explained in [4]. The combination of DLs with circumscription [3] provides a powerful and flexible alternative way for nonmonotonic reasoning in DLs since its entailment relation is parametrized with a set of concepts to be circumscribed. Hence we can pick different modes of defeasibility without changing our knowledge base. Decidablity and complexity are known for various DLs with circumscription [3], but no calculus or implementation is known. The integration of DLs with logic programming (LP) using MKNF [11] is closely related to DL-MKNF. They differ in expressive power since LP rules can make use of arbitrarily connected variables, yet these variables are all quantified in the same way. In contrast, DL-MKNF allows modal operators appearing in existential and universal restrictions. An exact comparison of this relationship is part of our future work. A tableau algorithm for the combination of the basic DL ALC [15] with MKNF (ALCKNF ) has been described in [4]. As mentioned in [4], ALCKNF can capture certain kinds of defaults and integrity constraints (ICs). For example, our example default regarding the location of the heart in humans can be formalised

Abstract: This work explores some aspects of a new and natural semantical dimension that can be accommodated within the syntax of description logics which opens up when passing from the classical truth-value interpretation to a constructive interpretation. We argue that such a strengthened interpretation is essential to represent applications with partial information adequately and to achieve consistency under abstraction as well as robustness under refinement. We introduce a constructive version of $\mathcal{ALC}$ , called ${c\mathcal{ALC}}$ , for which we give a sound and complete Hilbert axiomatisation and a Gentzen tableau calculus showing finite model property and decidability.

Abstract: Description Logics are a family of very expressive logics but some forms of knowledge are much more intuitive to formulate otherwise, say, as rules. Rules in DL can be dealt with two approaches: (i) use rules as they are knowing that it leads to undecidability. (ii) or make the rules DL-safe, which will restrict their semantic impact and, e.g., loose the nice “car owners are engine owners” inference. Here, we offer a third possibility: we rewrite the rule, if it satisfies certain restrictions, into a set of axioms which preserves the nice inferences. In this paper, we describe the rewriting technique and prove that it does really preserve the semantics of the rule. We have implemented the rewriting algorithm and have practical results.

Abstract: We have shown recently that, in extensions of ALC that involve inverse roles, conjunctive query answering is harder than satisfiability: it is 2-ExpTime-complete in general and NExpTime-hard if queries are connected and contain at least one answer variable [9]. In this paper, we show that, in SHIQ without inverse roles (and without transitive roles in the query), conjunctive query answering is only ExpTime-complete and thus not harder than satisfiability. We also show that the NExpTime-lower bound from [9] is tight.

Abstract: We propose an approach for extending a tableau-based satisfiability algorithm by an arithmetic component. The result is a hybrid concept satisfiability algorithm for the Description Logic (DL) ALCQ which extends ALC with qualified number restrictions. The hybrid approach ensures a more informed calculus which, on the one hand, adequately handles the interaction between numerical and logical restrictions of descriptions, and on the other hand, when applied is a very promising framework for average case optimizations.

Abstract: The use of Description Logic as the basis for Semantic Web Languages has led to new requirements with respect to scalable and nonstandard reasoning. In this paper, we address the problem of scalable reasoning by proposing a distributed, complete and terminating algorithm that decides satisfiability of terminologies in ALC. The algorithm is based on recent results on applying resolution to description logics. We show that the resolution procedure proposed by Tammet can be distributed amongst multiple resolution solvers by assigning unique sets of literals to individual solvers. This results provides the basis for a highly scalable reasoning infrastructure for Description logics.

Abstract: The invention relates to a self locking container comprising an integral tray and cover. Both the tray and cover are assembled without adhesive by tab and slot combinations provided in the walls thereof. In addition, the tab and slot combination for securing and locking the cover portion also serves as an automatic locking device for locking the cover to the tray when the container is closed.

Abstract: – The module extraction problem: given a terminology T1 and a signature Σ, extract from T1 a minimal self-contained terminology T0 such that T1 and T0 imply the same dependencies between Σ-terms. – The logical diff problem: given a signature Σ and two versions T0 and T1 of a terminology, check whether T0 and T1 are logically different in the sense that they do not imply the same dependencies between Σ-terms.

Abstract: In this paper, we present a normal form for concept expressions in the description logic ALC which is based on a recently introduced notion of prime implicate for the modal logic K. We show that concepts in prime implicate normal form enjoy a number of desirable properties which make prime implicate normal form interesting from the viewpoint of knowledge compilation. In particular, we prove that subsumption between ALC concepts in prime implicate normal form can be carried out in polynomial time using a simple structural subsumption algorithm reminiscent of those used for less expressive description logics. Of course, in order to take advantage of these properties, we need a way to transform concepts into equivalent concepts in prime implicate normal form. We provide a sound and complete algorithm for putting concepts into prime implicate normal form, and we investigate the spatial complexity of this transformation, showing there to be an at most doubly-exponential blowup in concept length. At the end of the paper, we compare prime implicate normal form to two other normal forms for ALC, discussing the relative merits of the different approaches.

Abstract: In this paper we consider the extensions of description logics that were proposed to represent uncertain or vague knowledge, focusing on the fuzzy and possibilistic formalisms. We compare these two approaches and comment on their differences concentrating on the consistency issue of knowledge bases represented in these extended frameworks. We present a classification of existing algorithms and describe a new method for the possibilistic case that yields an inconsistency degree and not only a binary answer to the consistency question. The proposed algorithm is based on a direct extension of the tableau algorithm to the possibilistic case, for which we introduce appropriate clash and completion rule definitions.

Abstract: Representing probabilistic knowledge in combination with a description logic has been a research topic for quite some time. In [1] one of such combinations is introduced. We present our implementation of the proposed system and some modeling observations we made.

Abstract: One of the most frequently used inference services of description logic reasoners is the classification of TBoxes with a subsumption hierarchy of all named concepts as the result. In response to (i) emerging TBoxes from the semantic web community consisting of up to hundreds of thousand of named concepts and (ii) the increasing availability of multi-processor and multior many-core computers, we propose a parallel approach for TBox classification. First experiments on parallelizing well-known algorithms for TBox classification were conducted to study the trade-off between incompleteness and speed improvement.

Abstract: Absorptions are generally employed in Description Logics (DL) reasoners in a uniform way regardless of the structure of an input knowledge base. In this paper we present an approach to encode some state-of-the-art absorption techniques into a state space planner, aiming to achieve a better solution. The planner applies appropriate operators to general axioms and produces a solution with a minimized cost to automatically organize these absorptions in a certain sequence to facilitate DL reasoning. Compared to predetermined or fixed applications of established absorptions, such a solution is more flexible and probable to absorb more general axioms into an unfoldable TBox.

Abstract: The paper summarizes our experiences with optimization techniques for well-known tableau-based description logic reasoning systems, and analyzes the performance of very simple techniques to cope with Tboxes whose bulk axioms just use a less expressive language such as ELH, whereas some small parts of the Tbox use a language as expressive as SHIQ. The techniques analyzed in this paper have been tested with RacerPro, but they can be embedded into other tableau-based reasoners such as, e.g., Fact++ or Pellet in a seamless way.

Abstract: In this paper, we propose a new method for revising terminologies in description logic-based ontologies. Our revision method is a reformulation of the kernel revision operator in belief revision. We first define our revision operator for terminologies in terms of MIPS (minimal incoherence-preserving sub-terminologies), and we show that it satisfies some desirable logical properties. Second, two concrete algorithms are developed to implement the revision operator.

Abstract: A recurring problem in conceptual modelling and ontology development is the representation of part-whole relations, with a requirement to be able to distinguish between essential and mandatory parts. To solve this problem, we formally characterize the semantics of these shareability notions by resorting to the temporal conceptual model ERV T and its formalization in the description logic DLRUS .

Abstract: The benefits of using an ontology over relational data sources to mediate the access to these data are widely accepted and well understood. Such ontologies provide a conceptual view of the application domain, therefore they can be conveniently employed for navigational (and reasoning) purposes when accessing the data [1]. To date, however, the task of wrapping relational data sources by means of an ontology is mainly done manually and is thus time-consuming and expensive process. We concentrate in this work on techniques towards an automatic support for ontology design in the scenario where the resulting ontology is used to access the data residing at the sources. Specifically, within this research area we identify two key tasks that we discuss next. Due to the wide use of relational databases in information management, their structure contains a lot of considerable information about domain of interest (e.g., in the scenario of enterprise integration). Therefore, when an ontology about the same domain is being designed, it is desirable to re-use this existing information and extract automatically a core ontology from the database schema, rather than constructing it from scratch. We tackle this issue by defining a framework for ontology extraction that integrates and enhances database reverse engineering techniques (see Section 2), giving us a faithful and higher level specification of the knowledge present in the given database. In order to fully leverage the obtained ontology for accessing the data, it is necessary to preserve the mapping between data sources and ontology. Our approach is to define and associate a view over the source data to each element of the ontology, which means that queries formulated over the extracted ontology can be simply evaluated by expanding the corresponding views. However, as soon as the extracted ontology is modified, the simple expansion is no longer enough and the newly added constraints and terms must be taken into account. Using an appropriate ontology language, this can be done by means of query rewriting techniques (see [2]). In most of the cases extracted ontologies are rather “flat”, and constitute a bare bootstrap ontology rather than a rich vocabulary enabling enhanced data access. For this reason, the task of enriching the extracted ontology is crucial in order to build a truly effective ontology-based information access system. The task of modifying a given ontology involves at least the introduction of

Abstract: Answering conjunctive queries (CQs) has been recognized as a key task for the usage of Description Logics (DLs) in a number of applications. The problem has been studied by many authors, who developed a number of different techniques for it. We present a novel method for CQ answering based on knots, which are schematic trees of depth ≤ 1. It yields an algorithm for CQ answering that works in exponential time for ALCH and for large classes of CQs in SH. This improves over previous algorithms which require double exponential time and is worst-case optimal, as already satisfiability testing in ALC is EXPTIMEcomplete. Our result reconfirms Lutz’s result that inverse roles cause an exponential jump in complexity, being the problem 2EXPTIME-complete for ALCI. The algorithm is CONP, and hence also worst-case optimal, under data complexity.

Abstract: In professional environments, users have a good knowledge about their domain of interest as well as the documents they consult regularly. In order to carry out their professional tasks, they need an Information Retrieval System (IRS) that allows them to find a precise answer to their information needs. Generally speaking, they know about documents content that may satisfy their information needs. Thus, during the retrieval task, they try to complete the information that they have and that is insufficient. Their information needs are in this case formulated through precise queries. The qualifier ”precise” denotes a query that contains: i) a very specialised terminology and ii) a complex structure. Through a precise query, a user can describe his information need using explicit semantic relationships between the descriptors of his query. He also can use boolean operators or quantification (at least, all, etc.) in order to specify the number of elements that the desired document should contain. In order to illustrate some characteristics of precise queries, we present here some query examples.

Abstract: We introduce an automata-based method for deciding the consistency of SHOQ⊓ knowledge bases. The presented algorithm decides knowledge base consistency in deterministic double exponential time for SHOQ⊓, but is in ExpTime if no role conjunctions occur in the input knowledge base. This shows that SHOQ is indeed ExpTimecomplete, which was, to the best of our knowledge, always conjectured but never proved.

Abstract: Hybrid EL-TBoxes combine general concept inclusions (GCIs), which are interpreted with descriptive semantics, with cyclic concept definitions, which are interpreted with greatest fixpoint (gfp) semantics We introduce a proof-theoretic approach that yields a polynomial-time decision procedure for subsumption in EL wrt hybrid TBoxes, and present preliminary experimental results regarding the performance of the reasoner Hyb that implements this decision procedure

Abstract: Many visualization frameworks for ontologies in general and for concept expressions in particular are too faithful to the syntax of the languages in which those objects are represented (e.g., RDF, OWL, DL). Model outlines depart from this tradition in that they consist of diagrams characterizing the class of models of a given concept expression. We hope this semantically-oriented visualization strategy will allow users to obtain deeper insights about the meaning of such expressions, thereby preventing errors of design or of interpretation.

Abstract: The development of scalable reasoning systems is one of the crucial factors determining the success of Semantic Web systems. Recently, in [GH06], an approach is proposed, which tackles the problem by splitting the assertional part of ontologies into several partitions. In this work we provide our experiences gained by implementing and understanding the given partitioning algorithm and fix some issues which came our way. Furthermore, we propose an extension of the algorithm, which allows for assertional updates, without need to repartition the whole knowledge base. Both contributions can hopefully increase the potential success of partitioning real world ontologies..

Abstract: Classical action formalisms form a dichotomy regarding their expressive power and computational properties: they are either based on first-order logic (FOL) and undecidable like the Situation Calculus [13], or decidable but only propositional like STRIPS [8, 7]. In [3, 11], it was proposed to integrate description logics (DLs) into action formalisms in order to increase the expressive power beyond propositional logic while retaining decidability of reasoning. In particular, ABox assertions are used for describing the initial state of the world and the preand post-conditions of actions, and acyclic TBoxes are used to describe background knowledge. A similar approach based on the 2-variable fragment of FOL is described in [9]. The results in [3] show that, even if expressive DLs such as ALCQIO are used in the action formalism, standard reasoning problems such as executability and projection remain decidable. The proof is by a reduction of these problems in a DL L to instance checking in the extension LO of L with nominals, and it works for all standard extensions of the propositionally closed DL ALC. A recent trend in description logic is to consider lightweight DLs that are not propositionally closed and for which standard reasoning problems such as subsumption and instance checking are tractable. In particular, the EL-family of DLs has been developed in [1, 6, 2, 4], and it has proved useful for modelling life science ontologies such as SNOMED [16] and the National Cancer Institute’s NCI thesaurus [15]. Many such ontologies are acyclic TBoxes and can thus be used in a DL-based action formalism. This paves the way to new applications such as the following: one can use ABoxes to describe patient data in the medical domain, actions to represent medical treatments, and in both cases use concepts defined in an underlying medical ontology. Executability and projection can then determine, e.g., whether a certain treatment is effective or has undesired sideeffects. In this paper, we investigate the complexity of executability and projection in EL and EL, the extension of EL with atomic negation. In both cases, we allow for negated assertions in the post-conditions of actions. Our results show that, in general, tractability does not transfer from instance checking to executability and projection. Even in EL without TBoxes, the latter problems are

Abstract: Recent years have seen a boom in the creation and development of ontologies. Unfortunately, the maintenance of such ontologies is an error-prone process. On one side, it is in general unrealistic to expect a developer to be simultaneously a domainand an ontology-expert. This leads to problems when a part of the domain is not correctly understood, or when, although correctly understood, is translated wrongly to the ontology language. On the other side, most of the larger ontologies are developed by a group of individuals. The difference in their points of view can produce unexpected consequences. Whenever an error is identified, one would like to be able to detect the portion of the ontology responsible for such it; additionally, it would also be desirable to modify the ontology as little as possible to remove the error. If, for instance, an ontology is expresed by a TBox of an expressive Description Logic (DL), an unwanted consequence could be the unsatisfiability of a certain concept term C. Given that C is indeed unsatisfiable, we can search for a minimal sub-TBox that still leads to unsatisfiability of the concept (explaining the consequence), or for a maximal sub-TBox where C is satisfiable (removing the consequence). Finding these sets by hand in large ontologies is not a viable option. Schlobach and Cornet [14] describe an algorithm for computing the minimal subsets of an unfoldable ALC-terminology that keep the unsatisfiability of a concept. The algorithm extends the known tableau-based satisfiability algorithm for ALC [15], using labels to keep track of the axioms responsible of the generation of an assertion during the execution of the algorithm. A similar approach was actually presented previously in [2], for checking consistency of ALC-ABoxes. The main difference between the algorithms in [14] and [2] is that the latter does not directly compute the minimal subsets that have the consequence, but rather a Boolean formula, called pinpointing formula, whose minimal satisfying valuations correspond to the minimal sub-ABoxes that are inconsistent. The ideas sketched by these algorithms have been applied to other tableau-based decision algorithms for more expressive DLs (see, e.g. [13, 12, 11]), and generalized in [3] where so-called general tableaux are extended into pinpointing algorithms that compute a formula as in [2]. This general approach was then successfuly applied for explaining subsumption relations in EL [4]. The main drawback of the general approach in [3] is that it assumes that the original tableau algorithm stops after a finite number of steps without the

Abstract: Most of the research on temporalized Description Logics (DLs) has concentrated on the case where temporal operators can be applied to concepts, and sometimes additionally to TBox axioms and ABox assertions. The aim of this article is to study temporalized DLs where temporal operators on TBox axioms and ABox assertions are available, but temporal operators on concepts are not. While the main application of existing temporalized DLs is the representation of conceptual models that explicitly incorporate temporal aspects, the family of DLs studied in this article addresses applications that focus on the temporal evolution of data and of ontologies. Our results show that disallowing temporal operators on concepts can significantly decrease the complexity of reasoning. In particular, reasoning with rigid roles (whose interpretation does not change over time) is typically undecidable without such a syntactic restriction, whereas our logics are decidable in elementary time even in the presence of rigid roles. We analyze the effects on computational complexity of dropping rigid roles, dropping rigid concepts, replacing temporal TBoxes with global ones, and restricting the set of available temporal operators. In this way, we obtain a novel family of temporalized DLs whose complexity ranges from 2- ExpTime-complete via NExpTime-complete to ExpTime-complete.

Abstract: Following the approaches and motivations given in recent works about action languages over description logics, we propose an action formalism based on a constructive semantics for ALC

Abstract: Knowledge base completion is a method for extending both the terminological and assertional part of a Description Logic knowledge base by using information provided by a domain expert. It ensures that the extended knowledge base is complete w.r.t. a fixed interpretation in a certain, well-defined sense. Here we consider the problem of explaining user errors in knowledge base completion. We show that for this setting, the problem of deciding the existence of an explanation within a specified cardinality bound is NP-complete, and the problem of counting explanations that are minimal w.r.t. set inclusion is #P-complete. We also provide an algorithm that computes one minimal explanation by performing at most polynomially many subsumption tests.