×

zbMATH — the first resource for mathematics

Cardinality restrictions on concepts. (English) Zbl 0907.68181
Summary: The concept description formalisms of existing description logics systems allow the user to express local cardinality restrictions on the fillers of a particular role. It is not possible, however, to introduce global restrictions on the number of instances of a given concept. This article argues that such cardinality restrictions on concepts are of importance in applications such as configuration of technical systems, an application domain of description logics systems that is currently gaining in interest. It shows that including such restrictions in the description language leaves the important inference problems such as instance testing decidable. The algorithm combines and simplifies the ideas developed for the treatment of qualified number restrictions and of general terminological axioms.

MSC:
68T30 Knowledge representation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baader, F., Augmenting concept languages by transitive closure of roles: an alternative to terminological cycles, () · Zbl 0742.68064
[2] Baader, F.; Bürckert, H.-J.; Hollunder, B.; Nutt, W.; Siekmann, J.H., Concept logics, ()
[3] Baader, F.; Hanschke, P., A scheme for integrating concrete domains into concept languages, () · Zbl 0742.68063
[4] Baader, F.; Hollunder, B., A terminological knowledge representation system with complete inference algorithms, ()
[5] Bagnasco, C.; Petrin, P.; Spampinato, L., Taxonomic reasoning in configuration tasks, ()
[6] Barwise, J.; Cooper, R., Generalized quantifiers and natural language, Linguist. philos., 4, 159-219, (1981) · Zbl 0473.03033
[7] Brachman, R.J.; Bobrow, R.J.; Cohen, P.R.; Klovstad, J.W.; Webber, B.L.; Woods, W.A., Research in natural language understanding, annual report, ()
[8] Buchheit, M.; Donini, F.M.; Schaerf, A., Decidable reasoning in terminological knowledge representation systems, J. artif. intell. res., 1, 109-138, (1993) · Zbl 0900.68396
[9] Buchheit, M.; Klein, R.; Nutt, W., Configuration as model construction: the constructive problem solving approach, ()
[10] Buchheit, M.; Klein, R.; Nutt, W., Constructive problem solving: a model construction approach towards configuration, ()
[11] Hollunder, B.; Baader, F., Qualifying number restrictions in concept languages, () · Zbl 0765.68190
[12] Klein, R., Model representation and taxonomic reasoning in configuration problem solving, ()
[13] McGuinness, D.L.; Resnick, L.A., Description logic-based configuration for consumers, ()
[14] Nebel, B., Reasoning and revision in hybrid representation systems, () · Zbl 0702.68095
[15] Owsnicki-Klewe, B., Configuration as a consistency maintenance task, () · Zbl 0747.68082
[16] Quantz, J., How to fit generalized quantifiers into terminological logics, (), 543-547
[17] Schild, K., Terminological cycles and the prepositional μ-calculus, ()
[18] van der Hoek, W.; De Rijke, M., Generalized quantifiers and modal logic, J. logic lang. inform., 2, 19-58, (1993) · Zbl 0797.03014
[19] Weida, R., Closing the terminology, ()
[20] Wright, J.R.; McGuinness, D.L.; Foster, C.; Vesonder, G.T., Conceptual modeling using knowledge representation: configurator applications, ()
[21] Wright, J.R.; Weixelbaum, E.S.; Brown, K.; Vesonder, G.T.; Palmer, S.R.; Herman, J.I.; Moore, H.H., A knowledge-based configurator that supports sales, engineering and manufacturing at AT&T network systems, AI mag., 14, 3, 69-80, (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.