Computing Least Common Subsumers in ALEN

Computing the least common subsumer (lcs) in description logics is an inference task first introduced for sublanguages of CLASSIC. Roughly speaking, the lcs of a set of concept descriptions is the most specific concept description that subsumes all of the input descriptions. As such, the lcs allows to extract the commonalities from given concept descriptions, a task essential for several applications like, e.g., inductive learning, information retrieval, or the bottom-up construction of KR-knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an lcs algorithm for the description logic ALEN, which allows for both constructors (as well as concept conjunction, primitive negation, and value restrictions). The proof of correctness of our lcs algorithm is based on an appropriate structural characterization of subsumption in ALEN also introduced in this paper.This research was carried out while the second author was still at the LuFG Theoretical Computer Science, RWTH Aachen

Structural Subsumption for ALN

Aus der Einleitung: „In this paper, we reuse the representation formalism `description graph' in order to characterize subsumption of ALN-concepts. The description logic ALN allows for conjunction, valuerestrictions, number restrictions, and primitive negation. Since Classic allows for more constructors than ALN, e.g., equality restrictions an attribute chains by the constructor SAME-AS,we can confine the notion of description graphs from [BP94]. On the other hand, ALN explicitly allows for primitive negation which yields another possibility { besides conflicting number restrictions { to express inconsistency. Thus, we have to modify the notion of canonical description graphs in order to cope with inconsistent concepts in the structural characterization of subsumption. It turns out that the description graphs obtained from ALN-concepts are in fact trees. A canonical graph is a deterministic tree. The conditions required by the structural characterization of subsumption on these trees can be tested by an eficient algorithm, i.e., we obtain an algorithm deciding subsumption of C and D in time polynomial in the size of C and D. The report is structured as follows. In the preliminaries, we define syntax and semantics of the description logic ALN as well as the inference problem of subsumption. In Section 3, we introduce description graphs, the data structure our structural subsumption algorithm is working on. Besides syntax and semantics also an algorithm for translating ALN-concepts into description graphs is given. Thereafter, we present the main result of this report in Section 6, a characterization of subsumption of ALN-concepts by a structural comparison of corresponding description graphs. Furthermore, a structural subsumption algorithm can be found in Section 6.2. In the last section we summarize our results and give an outlook to further applications of structural subsumption in terminological knowledge representation systems

A Description Logic for Vague Knowledge

This work introduces the concept language ALCFM which is an extension of ALC to many-valued logics. ALCFM allows to express vague concepts, e.g. more or less enlarged or very small. To realize this extension to many-valued logics, the classical notions of satisfiability and subsumption had to be modied appropriately. For example, ALCFM-concepts are no longer either satisfiable or unsatisfiable, but they are satisfiable to a certain degree. The main contribution of this paper is a sound and complete method for computing the degree of subsumption between two ALCFM-concepts.An abridged version of this paper has been published in the Proceedings of the 13th biennial European Conference on Artificial Intelligence (ECAI'98)

On the Relation between Conceptual Graphs and Description Logics

Aus der Einleitung: 'Conceptual graphs (CGs) are an expressive formalism for representing knowledge about an application domain in a graphical way. Since CGs can express all of first-order predicate logic (FO), they can also be seen as a graphical notation for FO formulae. In knowledge representation, one is usually not only interested in representing knowledge, one also wants to reason about the represented knowledge. For CGs, one is, for example, interested in validity of a given graph, and in the question whether one graph subsumes another one. Because of the expressiveness of the CG formalism, these reasoning problems are undecidable for general CGs. In the literature [Sow84, Wer95, KS97] one can find complete calculi for validity of CGs, but implementations of these calculi have the same problems as theorem provers for FO: they may not terminate for formulae that are not valid, and they are very ineficient. To overcome this problem, one can either employ incomplete reasoners, or try to find decidable (or even tractable) fragments of the formalism. This paper investigates the second alternative. The most prominent decidable fragment of CGs is the class of simple conceptual graphs (SGs), which corresponds to the conjunctive, positive, and existential fragment of FO (i.e., existentially quantified conjunctions of atoms). Even for this simple fragment, however, subsumption is still an NP-complete problem [CM92]. SGs that are trees provide for a tractable fragment of SGs, i.e., a class of simple conceptual graphs for which subsumption can be decided in polynomial time [MC93]. In this report, we will identify a tractable fragment of SGs that is larger than the class of trees. Instead of trying to prove new decidability or tractability results for CGs from scratch, our idea was to transfer decidability results from description logics [DLNN97, DLNS96] to CGs. The goal was to obtain a \natural' sub-class of the class of all CGs in the sense that, on the one hand, this sub-class is defined directly by syntactic restrictions on the graphs, and not by conditions on the first-order formulae obtained by translating CGs into FO, and, on the other hand, is in some sense equivalent to a more or less expressive description logic. Although description logics (DLs) and CGs are employed in very similar applications (e.g., for representing the semantics of natural language sentences), it turned out that these two formalisms are quite different for several reasons: (1) conceptual graphs are interpreted as closed FO formulae, whereas DL concept descriptions are interpreted by formulae with one free variable; (2) DLs do not allow for relations of arity > 2 ; (3) SGs are interpreted by existential sentences, whereas almost all DLs considered in the literature allow for universal quantification; (4) because DLs use a variable-free syntax, certain identifications of variables expressed by cycles in SGs and by co-reference links in CGs cannot be expressed in DLs. As a consequence of these differences, we could not identify a natural fragment of CGs corresponding to an expressive DL whose decidability was already shown in the literature. We could, however, obtain a new tractability result for a DL corresponding to SGs that are trees. This correspondence result strictly extends the one in [CF98]. In addition, we have extended the tractability result from SGs that are trees to SGs that can be transformed into trees using a certain \cycle-cutting' operation. The report is structured as follows. We first introduce the description logic for which we will identify a subclass of equivalent SGs. In Section 3, we recall basic definitions and results on SGs. Thereafter, we introduce a syntactical variant of SGs which allows for directly encoding the support into the graphs (Section 4.1). In order to formalize the equivalence between DLs and SGs, we have to consider SGs with one distinguished node called root (Section 4.2). In Section 5, we finally identify a class of SGs corresponding to a DL that is a strict extension of the DL considered in [CF98]

Die Zukunft der Regionen in Nordrhein-Westfalen gestalten: Eine gemeinsame Aufgabe von Regionalplanung und Regionalentwicklung

In NRW haben sowohl die Regionalplanung als auch integrierte Ansätze der Regionalentwicklung, wie z.B. die REGIONALE NRW, eine lange Tradition. Das bisherige Nebeneinander soll im Sinne eines besseren Zusammenwirkens von Regionalplanung und Regionalentwicklung mit dem Ziel eines "guten Raumzustandes" überwunden werden. Elemente einer neuen Praxis könnten etwa ein "Brückendokument" (z.B. Raumbild) zur Vermittlung zwischen Regionalplanung und -entwicklung sowie eine eigenständig handlungsfähige organisatorische Verankerung des Prozessmanagements sein. Unabdingbar dafür sind eine entsprechende politische Legitimation und ein Wille zur regionalen Zusammenarbeit.In NRW, both regional planning and integrated approaches to regional development, such as the REGIONALE NRW, have a long tradition. These two fields have previously existed in parallel, a situation that should be overcome through the better interaction of regional planning and regional development with the goal of creating "good spatial conditions". Elements of a new practice approach could include a "bridging document" (e.g. spatial vision) to mediate between regional planning and development, and also independent, empowered and organisationally anchored process management. Indispensable here are the appropriate political legitimacy and a will for regional cooperation

Unterstützung der Modellierung verfahrenstechnischer Prozesse durch Nicht-Standardinferenzen in Beschreibungslogiken

In chemical process engineering, as in many other application domains, one is interested in a structured representation and storage of domain specific knowledge. As shown in a cooperation between the Department for Process Engineering and the Teaching and Research Area for Theoreticel Computer Science, terminological knowledge representation systems based on description logics can be used for that purpose. Such systems are based on description logics, a highly expressive formalism with well-defined semantics, and provide powerful inference services like computing subconcept-/superconcept relationships. It has turned out, however, that these standard inference services are not sufficient for effectively supporting the maintenance of the knowledge base. In this work the non-standard inference services least common subsumer, most specific concept, and rewriting are investigated. Interacting in a certain way, these services provide a more comprehensive support for the definition of new concepts and thus support the extension and maintenance of the knowledge base. Results on existence, computability, and complexity are presented as well as algorithms for solving these inference problems for description logics that have already been successfully applied in the chemical process engineering application

Computing Most Specific Concepts in Description Logics with Existential Restrictions

Computing the most specific concept (msc) is an inference task that can be used to support the 'bottom-up' construction of knowledge bases for KR systems based on description logics. For description logics that allow for number restrictions or existential restrictions, the msc need not exist, though. Previous work on this problem has concentrated on description logics that allow for universal value restrictions and number restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. More precisely, we show that, for the description logic ALE (which allows for conjunction, universal value restrictions, existential restrictions, negation of atomic concepts) the msc of an ABox-individual only exists in case of acyclic ABoxes. For cyclic ABoxes, we show how to compute an approximation of the msc. Our approach for computing the (approximation of the) msc is based on representing concept descriptions by certain trees and ABoxes by certain graphs, and then characterizing instance relationships by homomorphisms from trees into graphs. The msc/approximation operation then mainly corresponds to unraveling the graphs into trees and translating them back into concept descriptions

Computing Least Common Subsumers in ALEN

Computing the least common subsumer (lcs) in description logics is an inference task first introduced for sublanguages of CLASSIC. Roughly speaking, the lcs of a set of concept descriptions is the most specific concept description that subsumes all of the input descriptions. As such, the lcs allows to extract the commonalities from given concept descriptions, a task essential for several applications like, e.g., inductive learning, information retrieval, or the bottom-up construction of KR-knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an lcs algorithm for the description logic ALEN, which allows for both constructors (as well as concept conjunction, primitive negation, and value restrictions). The proof of correctness of our lcs algorithm is based on an appropriate structural characterization of subsumption in ALEN also introduced in this paper.This research was carried out while the second author was still at the LuFG Theoretical Computer Science, RWTH Aachen

Structural Subsumption for ALN

Aus der Einleitung: „In this paper, we reuse the representation formalism `description graph' in order to characterize subsumption of ALN-concepts. The description logic ALN allows for conjunction, valuerestrictions, number restrictions, and primitive negation. Since Classic allows for more constructors than ALN, e.g., equality restrictions an attribute chains by the constructor SAME-AS,we can confine the notion of description graphs from [BP94]. On the other hand, ALN explicitly allows for primitive negation which yields another possibility { besides conflicting number restrictions { to express inconsistency. Thus, we have to modify the notion of canonical description graphs in order to cope with inconsistent concepts in the structural characterization of subsumption. It turns out that the description graphs obtained from ALN-concepts are in fact trees. A canonical graph is a deterministic tree. The conditions required by the structural characterization of subsumption on these trees can be tested by an eficient algorithm, i.e., we obtain an algorithm deciding subsumption of C and D in time polynomial in the size of C and D. The report is structured as follows. In the preliminaries, we define syntax and semantics of the description logic ALN as well as the inference problem of subsumption. In Section 3, we introduce description graphs, the data structure our structural subsumption algorithm is working on. Besides syntax and semantics also an algorithm for translating ALN-concepts into description graphs is given. Thereafter, we present the main result of this report in Section 6, a characterization of subsumption of ALN-concepts by a structural comparison of corresponding description graphs. Furthermore, a structural subsumption algorithm can be found in Section 6.2. In the last section we summarize our results and give an outlook to further applications of structural subsumption in terminological knowledge representation systems