Abstract
Class relations are used whenever the semantics of entire classes are described, independently of single entities. This chapter focuses on class relations that define cardinality restrictions for a certain instance relation (e.g., a topological relation) between all entities of the involved classes. Typical examples are spatial semantic integrity constraints or ontologies of geospatial entity classes. Reasoning on such class relations allows for the detection of inconsistencies and redundancies in sets of class relations. Therefore the logical properties of the applied instance relations and those of the cardinality restrictions have to be considered, in particular symmetry and compositions, but also other inferences. The chapter provides a summary of research and a discussion of open issues for future work on class relation reasoning.
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Notes
- 1.
Please be aware that all edges in Fig. 5 represent class relations that define cardinality restrictions and not the inheritance/generalisation relation between the classes.
References
Allen JF (1983) Maintaining knowledge about temporal intervals. Commun ACM 26(11):832–843
Agarwal P (2005) Ontological considerations in GIScience. Int J Geogr Inf Sci 19(5):501–536
Baumeister J, Seipel D (2006) Verification and refactoring of ontologies with rules. In: Staab S, Svátek V (eds) Managing knowledge in a world of networks, 15th international conference, EKAW 2006, LNCS 4248. Springer, Podebrady, pp 82–95
Bittner T, Donnelly M, Smith B (2009) A spatio-temporal ontology for geographic information integration. Int J Geogr Inf Sci 23(6):765–798
Brachman RJ (1983) What IS-A is and isn’t: an analysis of taxonomic links in semantic networks. Computer 16(10):30–36
Cohn AG, Hazarika SM (2001) Qualitative spatial representation and reasoning: an overview. Fundamenta Informaticae 46(1–2):1–29
Donnelly M, Bittner T (2005) Spatial relations between classes of individuals. In: Cohn AG, Mark DM (eds) COSIT 2005. LNCS, vol 3693. Springer, Heidelberg, pp 182–199
Donnelly M, Bittner T, Rosse C (2006) A formal theory for spatial representation and reasoning in biomedical ontologies. Artif Intell Med 36(1):1–27
Egenhofer MJ, Herring J (1991) Categorizing binary topological relationships between regions, lines, and points in geographic databases. Technical report, Department of Surveying Engineering, University of Maine, Orono, ME
Egenhofer MJ, Frank AU (1992) Object-oriented modeling for GIS. J Urban Reg Inf Syst Assoc 4(2):3–19
Egenhofer MJ, Al-Taha KK (1992) Reasoning about gradual changes of topological relationships. In: Theories and methods of spatio-temporal reasoning in geographic space, International conference GIS—from space to territory: theories and methods of spatio-temporal reasoning, LNCS, vol 639, pp 196–219, Springer
Egenhofer M (1994) Deriving the composition of binary topological relations. J Vis Lang Comput 5(2):133–149
Egenhofer MJ, Mark DM (1995) Modelling conceptual neighbourhoods of toplogical line-region relations. Int J Geogr Inf Syst 9(5):555–565
Egenhofer M (2011) Reasoning with complements. In: De Troyer O, Bauzer Medeiros C, Billen R, Hallot P, Simitsis A, Van Mingroot H (eds) Advances in conceptual modeling. Recent developments and new directions; ER 2011, vol 6999 of Lecture notes in computer science. Springer, San Diego, pp 261–270
Frank AU (1992) Qualitative spatial reasoning about distances and directions in geographic space. J Vis Lang Comput 3:343–371
Freksa C (1991) Qualitative spatial reasoning. In: Mark DM, Frank AU (eds) Cognitive and linguistic aspects of geographic space. Kluwer Academic Press, Dordrecht, pp 361–372
Freksa C (1992a) Using orientation information for qualitative spatial reasoning. In: Frank AU et al (eds) Theories and methods of spatio-temporal reasoning in geographic space. LNCS, vol 639. Springer, Pisa, pp 162–178
Freksa C (1992b) Temporal reasoning based on semi-intervals. Artif Intell 54(1):199–227
Grigni M, Papadias D, Papadimitriou C (1995) Topological inference. In: Proceedings of the International Joint Conference of Artificial Intelligence (IJCAI), pp 901–906
Hernández D (1994) Qualitative representation of spatial knowledge, LNCS, vol 804 of Lecture notes in artifcial intelligence. Springer, Heidelberg
Hornsby K, Egenhofer MJ, Hayes PJ (1999) Modeling cyclic change. In: Chen PP et al (eds) Advances in conceptual modeling: Proceedings of ER ‘99 workshops on evolution and change in data management, reverse engineering in information systems, and the world wide web and conceptual modeling, LNCS, vol 1727. Springer, Paris, pp 98–109
Kurata Y, Egenhofer MJ (2006) The head-body-tail intersection for spatial relations between directed line segments. In: Raubal M et al (eds) Geographic information science, 4th international conference, LNCS, vol 4197. Springer, Berlin, pp 269–286
Mäs S, Wang F, Reinhardt W (2005) Using ontologies for integrity constraint definition. In: Wu L et al (eds) Proceedings of the 4th international symposium on spatial data quality, ISSDQ 2005, pp 304–313
Mäs S (2007) Reasoning on spatial semantic integrity constraints. In: Winter S et al (eds) COSIT 2007. LNCS, vol 4736. Springer, Heidelberg, pp 285–302
Mäs S (2008) Reasoning on spatial relations between entity classes. In: Cova TJ et al (eds) 5th international conference geographic information science (GIScience), Park City, Utah, USA; LNCS, vol 5266, pp 234–248
Mäs S (2009a) On the consistency of spatial semantic integrity constraints. PhD thesis, University of the Bundeswehr, Munich (published in: Dissertations in Geographic Information Science, GISDISS 004; IOS Press)
Mäs S (2009b) Harmonisation of spatial semantic integrity constraints. In: AGILE 2009 pre-conference workshop “challenges in geospatial data harmonisation”, Hannover, Germany
Mäs S, Reinhardt W (2009) Categories of geospatial and temporal integrity constraints. In: International conference on advanced geographic information systems and web services, GEOWS 2009, pp 146–151, IEEE Computer Society
Rodriguez A, de Weghe NV, Maeyer PD (2004) Simplifying sets of events by selecting temporal relations. In: Egenhofer MJ et al (eds) Geographic information science. Third international conference, GIScience 2004, LNCS, vol 3234. Springer, Heidelberg, pp 269–284
Tarquini F, Clementini E (2008) Spatial relations between classes as integrity constraints. Trans GIS 12(1):45–57
Acknowledgments
Parts of this chapter have been written while the author was working at the AGIS at the University of the Bundeswehr Munich, Germany. The support from Wolfgang Reinhardt during that time is gratefully acknowledged. Also, the author likes to acknowledge the fruitful discussions with Max J. Egenhofer. Thanks are due to the two anonymous reviewers for their suggestions and critical comments that helped to improve this chapter.
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Mäs, S. (2013). Reasoning on Class Relations: An Overview. In: Raubal, M., Mark, D., Frank, A. (eds) Cognitive and Linguistic Aspects of Geographic Space. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34359-9_13
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