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Granularity as a Parameter of Context

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3554))

Abstract

Spatial and temporal granularity can be understood as parameters of context restricting the set of accessible objects in a context. Starting from the idea that this selection process depends to a large extent on the relation between the grain-size of the context and the local extension of the objects, the granularity of a context is in this article formalised as a class of possible sizes in the context. This formalisation is shown to be in accordance to well-known mathematical foundations on perceptual classification. An example for the case of temporal granularity illustrates how the introduction of new elements into a context may result in a more or less smooth shifting of the granularity leading to a classification of four different types of change of granularity. The results can be applied in a wide range of fields, e.g. in research on contextual reasoning and natural language understanding.

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References

  1. Allen, J.: Towards a general theory of action and time. Artificial Intelligence 23, 123–154 (1984)

    Article  MATH  Google Scholar 

  2. Benerecetti, M., Bouquet, P., Ghidini, C.: Contextual reasoning distilled. Journal of Experimental and Theoretical Artificial Intelligence 12(3), 279–305 (2000)

    Article  MATH  Google Scholar 

  3. Bettini, C., Jajodia, S., Wang, X.S.: Time granularities in databases, data mining, and temporal reasoning. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  4. Bittner, T., Smith, B.: A theory of granular partitions. In: Duckham, M., Goodchild, M.F., Worboys, M.F. (eds.) Foundations of Geographic Information Science, pp. 117–151. Taylor & Francis, London (2003)

    Chapter  Google Scholar 

  5. Bittner, T., Stell, J.G.: Stratified rough sets and vagueness. In: Kuhn, W., Worboys, M., Timpf, S. (eds.) Spatial Information Theory: Foundations of Geographic Information Science, Berlin, pp. 270–286. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Fine, K.: Vagueness, truth, and logic. Synthese 30, 265–300 (1975)

    Article  MATH  Google Scholar 

  7. Franceschet, M., Montanari, A.: Branching within time: an expressively complete and elementarily decidable temporal logic for time granularity. Research on Language and Computation 1(3–4), 229–263 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Frank, A.: The prevalence of objects with sharp boundaries in GIS. In: Burrough, P., Frank, A. (eds.) Geographic Objects with Indeterminate Boundaries, pp. 29–40. Taylor & Francis, London (1996)

    Google Scholar 

  9. Galton, A.: Qualitative Spatial Change. Oxford University Press, Oxford (2000)

    Google Scholar 

  10. Goodchild, M.: A geographer looks at spatial information theory. In: Montello, D. (ed.) Spatial Information Theory: Foundations of Geographic Information Science, Berlin, pp. 1–13. Springer, Heidelberg (2001)

    Google Scholar 

  11. Halpern, J.Y.: Intransitivity and vagueness. In: Dubois, D., Welty, C.A., Williams, M.-A. (eds.) Principles of Knowledge Representation and Reasoning: Proc. 9th Intl. Conf (KR 2004), pp. 121–129. AAAI Press, Menlo Park (2004)

    Google Scholar 

  12. Herskovits, A.: Schematization. In: Olivier, P., Gapp, K.-P. (eds.) Representation and Processing of Spatial Expressions, Erlbaum, Mahwah, NJ, pp. 149–162 (1998)

    Google Scholar 

  13. Hobbs, J.: Granularity. In: Proceedings of IJCAI 1985, pp. 432–435 (1985)

    Google Scholar 

  14. Hyde, D.: Sorites paradox. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. CSLI (internet publication), Stanford, Ca., Fall (2002)

    Google Scholar 

  15. Kosslyn, S.: Image and Mind. The MIT Press, Cambridge (1980)

    Google Scholar 

  16. Krifka, M.: Be brief and vague! and how bidirectional optimality theory allows for verbosity and precision. In: Restle, D., Zaefferer, D. (eds.) Sounds and Systems. Studies in Structure and Change. A Festschrift for Theo Vennemann, pp. 439–458. Mouton de Gruyter, Berlin (2002)

    Google Scholar 

  17. Mourelatos, A.: Events, processes, and states. Linguistics and Philosophy 2, 415–434 (1978)

    Article  Google Scholar 

  18. Ohlbach, H.: Calendrical calculations with time partitionings and fuzzy time intervals. In: Ohlbach, H., Schaffert, S. (eds.) Principles and Practice of Semantic Web Reasoning: Second International Workshop, Berlin, pp. 118–133 (2004)

    Google Scholar 

  19. Ohlbach, H.J., Gabbay, D.M.: Calendar logic. Journal of Applied Non-Classical Logics 8(4) (1998)

    Google Scholar 

  20. Pawlak, Z.: Rough Sets. Kluwer, Dordrecht (1994)

    Google Scholar 

  21. Reitsma, F., Bittner, T.: Scale in object and process ontologies. In: Kuhn, W., Worboys, M.F., Timpf, S. (eds.) COSIT 2003. LNCS, vol. 2825, pp. 13–27. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. Schmidtke, H.: A geometry for places: Representing extension and extended objects. In: Kuhn, W., Worboys, M., Timpf, S. (eds.) Spatial Information Theory: Foundations of Geographic Information Science, Berlin, pp. 235–252. Springer, Heidelberg (2003)

    Google Scholar 

  23. Schmidtke, H.: Aggregations and constituents: geometric specification of multi-granular objects. Journal of Visual Languages and Computing (2005) (to appear)

    Google Scholar 

  24. Suppes, P., Zinnes, J.: Basic measurement theory. In: Luce, R., Bush, R., Galanter, E. (eds.) Handbook of Mathematical Psychology. John Wiley & Sons, New York (1963)

    Google Scholar 

  25. van Deemter, K.: The sorites fallacy and the context-dependence of vague predicates. In: Kanazawa, M., Pinon, C., de Swart, H. (eds.) Quantifiers, Deduction, and Context, pp. 59–86. CSLI Publications, Stanford (1995)

    Google Scholar 

  26. Varzi, A.: Vagueness. In: Nadel, L. (ed.) Encyclopedia of Cognitive Science, pp. 459–464. Macmillan and Nature Publishing Group, London (2003)

    Google Scholar 

  27. Zadeh, L.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland, Amsterdam (1979)

    Google Scholar 

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Schmidtke, H.R. (2005). Granularity as a Parameter of Context. In: Dey, A., Kokinov, B., Leake, D., Turner, R. (eds) Modeling and Using Context. CONTEXT 2005. Lecture Notes in Computer Science(), vol 3554. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11508373_34

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  • DOI: https://doi.org/10.1007/11508373_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26924-3

  • Online ISBN: 978-3-540-31890-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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