Abstract not found

Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because non-trivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows non-trivial interactions between the combined components. The new method, called E-connection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of E-connections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of n-ary ‘link relations. ’ We define several natural variants of E-connections and study in-depth the transfer of decidability from the component systems to their E-connections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.

Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building real-world applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms. 1 Introduction Description logics are knowledge representation and reasoning formalisms dealing with conceptual knowledge on an abstract logical level. However, for a variety of applications, it is essential to integrate the abstract knowledge with knowledge of a more concrete nature. Examples of such "co...

This paper introduces a new logical formalism, intended for temporal conceptual modelling, as a natural combination of the well-known description logic DLR and point-based linear temporal logic with Since and Until. We define a query language (where queries are non-recursive Datalog programs and atoms are complex DLR US expressions) and investigate the problem of checking query containment under the constraints defined by DLR US conceptual schemas, as well as the problems of schema satisfiability and logical implication. Although it is shown that reasoning in full DLR US is undecidable, we identify the decidable (in a sense, maximal) fragment DLR - US by allowing applications of temporal operators to formulas and entities only (but not to relation expressions) . We obtain the following hierarchy of complexity results: (a) reasoning in DLR - US with atomic formulas is EXPTIME-complete, (b) satisfiability and logical implication of arbitrary DLR - US formulas is EXPSPACE-complete, and (c) the problem of checking query containment of non-recursive Datalog queries under DLR - US constraints is decidable in 2EXPTIME. 1 1

This paper surveys the temporal extensions of Description Logics appearearing in the literature. The analysis considers a large spectrum of approaches appearearing in the Temporal Description Logics area: from the loosely coupled approaches { which comprise, for example, the enhancement of simple Description Logics with a constraint based mechanism { to the most principled ones { which consider a combined semantics for the abstract and the temporal domains. It will be shown how these latter approaches have a strict connection with temporal logics

This paper presents a method for reasoning about spatial objects and their qualitative spatial relationships. In contrast to existing work, which mainly focusses on reasoning about qualitative spatial relations alone, we integrate quantitative and qualitative information with terminological reasoning. For spatioterminological reasoning we present the description logic ALCRP(D) and define an appropriate concrete domain D for polygons. The theory is motivated as a basis for knowledge representation and query processing in the domain of deductive geographic information systems. 1 Introduction Qualitative relations play an important role in formal reasoning systems that can be part of, for instance, geographic information systems (GIS). In this context, inferences about spatial relations should not be considered in isolation but should be integrated with formal inferences about structural descriptions of domain objects (e.g. automatic consistency checking and classification) and infer...

. TBoxes in their various forms are key components of knowledge representation systems based on description logics (DLs) since they allow for a natural representation of terminological knowledge. Largely due to a classical result given by Nebel [15], complexity analyses for DLs have, until now, mostly failed to take into account the most basic form of TBoxes, so-called acyclic TBoxes. In this paper, we concentrate on DLs for which reasoning without TBoxes is PSpace-complete, and show that there exist logics for which the complexity of reasoning remains in PSpace if acyclic TBoxes are added and also logics for which the complexity increases. This demonstrates that it is necessary to take acyclic TBoxes into account for complexity analyses. 1 Introduction A core feature of description logics is their ability to represent and reason about terminological knowledge. Terminological knowledge is stored in so-called TBoxes which mainly come in two avours. So-called acyclic TBoxes are sets o...

Recent efforts in the Conceptual Modelling community have been devoted to properly capturing time-varying information. Various temporally enhanced Entity-Relationship (ER) models have been proposed that are intended to model the temporal aspects of database conceptual schemas. This work gives a logical formalisation of the various properties that characterise and extend different temporal ER models which are found in literature. The formalisation we propose is based on Description Logics (DL), which have been proved useful for a logical reconstruction of the most popular conceptual data modelling formalisms.

Until now, interval-based temporal Description Logics (DLs) did---if at all---only admit TBoxes of a very restricted form, namely acyclic macro definitions. In this paper, we present a temporal DL that overcomes this deficieny and combines intervalbased temporal reasoning with general TBoxes. We argue that this combination is very interesting for many application domains. An automata-based decision procedure is devised and a tight EXPTIMEcomplexity bound is obtained. Since the presented logic can be viewed as being equipped with a concrete domain, our results can be seen from a different perspective: we show that there exist interesting concrete domains for which reasoning with general TBoxes is decidable.

We survey temporal description logics that are based on standard temporal logics such as LTL and CTL. In particular, we concentrate on the computational complexity of the satisfiability problem and algorithms for deciding it.