{"type":"ScholarlyArticle","title":"A Scheme for Integrating Concrete Domains into Concept Languages","authors":[{"name":"Franz Baader","slug":"franz-baader","given":"Franz","family":"Baader","affiliation":"German Research Center for AI (DFKI) Postfach 2080 W-6750 Kaiserslautern , Germany"},{"name":"Philipp Hanschke","slug":"philipp-hanschke","given":"Philipp","family":"Hanschke","affiliation":"German Research Center for AI (DFKI) Postfach 2080 W-6750 Kaiserslautern , Germany"}],"abstract":"A drawback which concept languages based on KL-ONE have is that all the terminological knowledge has to be defined on an abstract logical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defining concepts. Examples for such concrete domains are the integers, the real numbers, or also non-arithmetic domains, and predicates could be equality, inequality, or more complex predicates . In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the important inference problems such as subsumption, instantiation, and consistency. The formal semantics as well as the reasoning algorithms can be given on the scheme level. In contrast to existing KL-ONE based systems, these algorithms are not only sound but also complete. They generate subtasks which have to be solved by a special purpose r·easoner of the concrete domain.","doi":null,"url":"https://ijcai.org/proceedings/1991/68","pdf":"https://ijcai.org/proceedings/1991/0068.pdf","markdown":"https://ijcai.org/proceedings/1991/68.md","bibtex":"https://ijcai.org/proceedings/1991/bibtex/68","volume":{"slug":"1991","title":"Proceedings of the Twelfth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 1991","url":"https://ijcai.org/proceedings/1991/","year":1991,"location":"Sydney, New South Wales, Australia","dates":"24-30 August 1991","editors":"John Mylopoulos and Ray Reiter","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Knowledge Representation","track":"Knowledge Representation","number":68,"pages":{"first":452,"last":456},"keywords":[],"videos":[],"references":[{"position":1,"raw":"[Baader and Hanschke, 1991] F. Baader and P. Han- schke. A scheme for integrating concrete domains into concept languages. Research Report RR-91-10, DFKI, Kaiserslautern, 1991.","title":"A scheme for integrating concrete domains into concept languages","authors":"F Baader, P Hanschke","year":"1991","venue":null,"doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Baader, 1990] F. Baader. Terminological cycles in KL- ONE-based knowledge representation languages. In Proceedings of the Eighth National Conference on A r- tificial Intelligence, volume 2, pages 621-626. AAAI, 1990.","title":"Terminological cycles in KL-ONE-based knowledge representation languages","authors":"F Baader","year":"1990","venue":"Proceedings of the Eighth National Conference on A rtificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Borgida et al., 1989] A. Borgida, R. J. Brachman, D. L. McGuinness, and L. A. Resnick. CLASSIC: A struc- tural data model for objects. In International Confer- ence on Management of Data. ACM SIGMOD, 1989.","title":"CLASSIC: A structural data model for objects","authors":"A Borgida, R J Brachman, D L Mcguinness, L A Resnick","year":"1989","venue":"International Conference on Management of Data","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Brachman and Schmolze, 1985] R. J. Brachman and J. G. Schmolze. An overview of the KL-ONE knowledge representation system. Cognitive Science, 9(2): 171- 216, 1985.","title":"An overview of the KL-ONE knowledge representation system","authors":"R J Brachman, J G Schmolze","year":"1985","venue":"Cognitive Science","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Brachman et al., 1979] R. J. Brachman, R. J. Bobrow, P.R. Cohen, J. W. Klovstad, B. L. Webber, and W. A. Woods. Research in natural language understanding, annual report. Tech. Rep. No. 4274, Cambrige, MA, 1979. Bolt Beranek and Newman. Brachman et al., 1985]","title":"Research in natural language understanding","authors":"R J Brachman, R J Bobrow, P R Cohen, J W Klovstad, B L Webber, W A Woods","year":"1979","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"R. J. Brachman, V. Pigman Gilbert, and H. J. Levesque. An essential hybrid rea- soning system: knowledge and symbol level accounts in KRYPTON. In Proceedings of the 9th International Joint Conference on Artificial Intelligence, pages 532- 539, 1985.","title":"An essential hybrid reasoning system: knowledge and symbol level accounts in KRYPTON","authors":"R J Brachman, V Pigman Gilbert, H J Levesque","year":"1985","venue":"Proceedings of the 9th International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Edelmann and Owsnicki, 1986] J. Edelmann and B. Owsnicki. Data models in knowledge representa- tion systems: a case study. In GWAI-86 und 2. Ostereichische Artificial-Intelligence-Tagung, volume 124 of Informatik-Fachberichte, pages 69-74. Springer, 1986.","title":"Data models in knowledge representation systems: a case study","authors":"J Edelmann, B Owsnicki","year":"1986","venue":"Ostereichische Artificial-Intelligence-Tagung","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Hollunder and Nutt, 1990] B. Hollunder and W. Nutt. Subsumption algorithms for concept languages. Re- search Report RR-90-04, DFKI, Kaiserslautern, 1990.","title":"Subsumption algorithms for concept languages","authors":"B Hollunder, W Nutt","year":"1990","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Hollunder et al., 1990] B. Hollunder, W. Nutt, and M. Schmidt-SchauB. Subsumption algorithms for con- cept description languages. In 9th European Confer- ence on Artificial Intelligence (ECAI'90}, pages 348- 353, 1990.","title":"Subsumption algorithms for concept description languages","authors":"B Hollunder, W Nutt, M Schmidt-Schaub","year":"1990","venue":"9th European Conference on Artificial Intelligence (ECAI'90}","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Hollunder, 1990] B. Hollunder. Hybrid inferences in KL-ONE-based knowledge representation systems. In GWAI-90; 14th German Workshop on Artificial In- telliqence, volume 251 of Informatik-Fachberichte, pages 38-47. Springer, 1990.","title":"Hybrid inferences in KL-ONE-based knowledge representation systems","authors":"B Hollunder","year":"1990","venue":"GWAI-90; 14th German Workshop on Artificial Intelliqence","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Kobsa, 1989] A. Kobsa. The SB-ONE knowledge repre- sentation workbench. In Preprints of the Workshop on Formal Aspects of Semantic Networks, 1989. Two Harbors, Cal.","title":"The SB-ONE knowledge representation workbench","authors":"A Kobsa","year":"1989","venue":"Preprints of the Workshop on Formal Aspects of Semantic Networks","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Lassez, 1987] C. Lassez . Constraint logic programming. In Constraint Logic Programming: A Reader, 1987. Fourth IEEE Symposium on Logic Programming, San Francisco.","title":"Constraint logic programming","authors":"C Lassez","year":"1987","venue":"Fourth IEEE Symposium on Logic Programming","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Levesque and Brachman, 1987] H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computa- tional Intelligence, 3:78-93, 1987.","title":"Expressiveness and tractability in knowledge representation and reasoning","authors":"H J Levesque, R J Brachman","year":"1987","venue":"Computational Intelligence","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Matijacevic, 1970] Y. Matijacevic. Enumerable sets are diophantine. Soviet Math . Doklady, 11:354-357, 1970. English translation.","title":"Enumerable sets are diophantine","authors":"Y Matijacevic","year":"1970","venue":"Soviet Math . Doklady","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Mays et al., 1988] E. Mays, C. Apte, J. Griesmer, and J. Kastner. Experience with K-Rep: an object cen- tered knowledge representation language. In Proceed- ings of IEEE CAIA-88, pages 62-67, 1988.","title":"Experience with K-Rep: an object centered knowledge representation language","authors":"E Mays, C Apte, J Griesmer, J Kastner","year":"1988","venue":"Proceedings of IEEE CAIA","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Nebel and von Luck, 1988] B. Nebel and K. von Luck. Hybrid reasoning in BACK. In Z. W . Ras and L. Saitta, editors, Methodologies for Intelligent Systems, vol- ume 3, pages 260-269. North-Holland, 1988.","title":"Hybrid reasoning in BACK","authors":"B Nebel, K Luck","year":"1988","venue":"Methodologies for Intelligent Systems","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Nebel, 1989] B. Nebel. Terminological cycles: Seman- tics and computational properties. In Proceedings of the Workshop on Formal Aspects of Semantic Net- works, 1989. Two Harbors, Cal.","title":"Terminological cycles: Semantics and computational properties","authors":"B Nebel","year":"1989","venue":"Proceedings of the Workshop on Formal Aspects of Semantic Networks","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Patel-Schneider et al., 1990] P. F. Patel-Schneider, B. Owsnicki-Klewe, A. Kobsa, N. Guarino, R. McGregor, W. S. Mark, D. McGui- ness, B. Nebel, A. Schmiedel, and J. Yen. Report on the workshop on term subsumption languages in knowledge representation. AI Magazine, 11(2):16-23, 1990.","title":"Report on the workshop on term subsumption languages in knowledge representation","authors":"P F Patel-Schneider, B Owsnicki-Klewe, A Kobsa, N Guarino, R Mcgregor, W S Mark, D Mcguiness, B Nebel, A Schmiedel, J Yen","year":"1990","venue":"AI Magazine","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Patel-Schneider, 1984] P. F. Patel-Schneider. Small can be beautiful in knowledge representation. In Proceedings of the IEEE Workshop on Principles of Knowledge-Based Systems, pages 11-16. Denver, Colo., 1984.","title":"Small can be beautiful in knowledge representation","authors":"P F Patel-Schneider","year":"1984","venue":"Proceedings of the IEEE Workshop on Principles of Knowledge-Based Systems","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Schmidt-SchauB and Smolka, 1991] M. Schmidt-SchauB and G. Smolka. Attributive con- cept descriptions with complements. To appear in Journal of Artificial Intelligence, 47, 1991.","title":"Attributive concept descriptions with complements","authors":"M Schmidt-Schaub, G Smolka","year":"1991","venue":"Journal of Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Schmidt-Schau6, 1989] M. Schmidt-Schau6. Subsump- tion in KL-ONE is undecidable. In R. J. Brachman, ed- itor, First International Conference on Principles of Knowledge Representation and Reasoning, pages 421- 431, 1989.","title":"Subsumption in KL-ONE is undecidable","authors":"M Schmidt-Schau6","year":"1989","venue":"First International Conference on Principles of Knowledge Representation and Reasoning","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Tarski, 1951] A. Tarski. A Decision Method for Ele- mentary Algebra and Geometry. U. of California Press. Berkley, 1951.","title":"A Decision Method for Elementary Algebra and Geometry","authors":"A Tarski","year":"1951","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Vilain, 1985] M. Vilain. The restricted language archi- tecture of a hybrid representation system. In Pro- ceedings of the 9th International Joint Conference on Artificial Intelligence, pages 547-551, 1985.","title":"The restricted language architecture of a hybrid representation system","authors":"M Vilain","year":"1985","venue":"Proceedings of the 9th International Joint Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":"/proceedings/1985/104"}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}