U. Sattler. The complexity of concept languages with different kinds of transitive roles. unpublished. Knowledge representation in process engineering 239  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of critical design requirements [ Nowlan, 1993 ] supports transitive roles and general concept inclusions (GCIs) The theory of extended tableaux calculus subsumption algorithms which are able to deal with transitive roles and GCIs is well understood [ Baader, 1990; Buchheit et al. 1993; Sattler, 1996; Schild, 1991 ] but severe worst case intractability appears to limit their practical applicability. However it seems worthwhile to investigate how well such an algorithm performs with a real knowledge base when a range of optimisations are employed. The adaption of heuristic speed up techniques ....

U. Sattler. The complexity of concept languages with different kinds of transitive roles. In G. Gorz and S. Holldobler, editors, 20. Deutsche Jahrestagung fur Kunstliche Intelligenz, number 1137 in Lecture Notes in Artificial Intelligence. Springer Verlag, 1996.

....x, y and z, xRy ySz ) xRz. Note that the special case where a role is specialised by itself results in a transitively closed role. Although there is no role forming operator for transitive closure, the combination of specialisation and the role hierarchy does allow transitive orbits of roles (Sattler 1996) to be defined. The range of use of transitive roles and specialisation in GALEN s ontology can be classified under two main headings, but the ramifications are surprisingly wide. ffl To express partitive and locative relationships in anatomy and causal and functional relationships in ....

.... to say that hollow objects may define a space (i.e. are sanctioned to de 2 The development of a common controlled vocabulary has been put forward as the number one grand challenge of Medical Informatics (Sittig 1994) 3 Or even the slightly less expressive transitive orbits of roles (Sattler 1996). fine a space) rather than that they necessarily define a space. Such statements might be usefully dropped from the ontology. As to other issues of modelling style, the limitation of the primitive type hierarchy to a strict hierarchy of disjoint types (except for well controlled cases at the ....

Sattler, U. 1996. The complexity of concept languages with different kinds of transitive roles. In Gorz, G., and Holldobler, S., eds., 20. Deutsche Jahrestagung fur Kunstliche Intelligenz, number 1137 in Lecture Notes in Artificial Intelligence. Springer Verlag.

.... constraints, which explains the need for concrete domains in this context [ Baader and Hanschke,1993 ] Extension by transitive closure: The adequate representation of the complex structure of technical systems necessitates the use of the part whole relationship in the concept descriptions [ Sattler,1995; 1996 ] This relationship cannot simply be described by a new binary relation (an atomic role in the terminological language) since important properties of part whole relations (like transitivity) would not be modeled this way. An extension of the terminological formalism by transitive closure of ....

U. Sattler. The complexity of concept languages with different kinds of transitive roles. In 20. Deutsche Jahrestagung fur Kunstliche Intelligenz, KI'96, Lecture Notes in Artificial Intelligence. Springer Verlag, 1996. To appear.

.... hypothesis that the general part whole relation should be modeled as a transitive role has part: For all interpretations I holds (x; y) 2 has part I and (y; z) 2 has part I implies (x; z) 2 has part I : It has still to be decided whether and which sub roles are additionally needed: In [25], it could be shown that extending ALC by transitive roles does not change its complexity dramatically (the satisfiability problem remains in Pspace) Role names are partitioned into one part containing roles that are interpreted as arbitrary roles and a second part whose elements have to be ....

U. Sattler. The complexity of concept languages with different kinds of transitive roles. unpublished. Knowledge representation in process engineering 239

....or along any (finite) number of decomposition levels. Hence an interesting question is, in which ways transitive relations can be included into description languages and handled by their inference algorithms. We investigated this question for an expressive, well known description language in [ Sattler,1996 ] Number restrictions: As for configuration problems, objects are often characterized by the number of objects they are related to by some relation. For example, we want to describe devices having at least 7 inputs or exactly 5 outputs. In description languages, this can be done using number ....

.... expressive for our application: We wanted to describe devices having the same number of inputs as of outputs, as in (device u ( ff input) u ( ff output) or devices having less inputs as each of its parts have, as in (device u ( ff input) u (8has part: ff input) In [ Baader and Sattler,1996a ] these symbolic number restrictions are introduced and investigated. Unfortunately, it turned out that the basic inference problems such as satisfiability or subsumption get very complex, even undecidable, if this kind of number restriction is allowed in a unrestricted way. Nevertheless, it ....

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U. Sattler. The complexity of concept languages with different kinds of transitive roles. In 20. Deutsche Jahrestagung fur Kunstliche Intelligenz, LNAI. Springer-Verlag, 1996. To appear.

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