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Distance constraint arrays: A model for reasoning on intervals with qualitative and quantitative distances

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Advances in Artificial Intelligence (Canadian AI 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1418))

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Abstract

We outline a model of one-dimensional reasoning on interval relations with quantitative and qualitative distances. At the core of this model lie constraints on interval boundaries, partial ordering and subsumption relations on interval relations and interval boundary constraints, and the transformation of interval relations to interval boundary constraints and vice versa. By way of subsumption and approximation criteria on distance constraint arrays, a significant level of conceptual abstraction from the underlying interval boundary constraints is realized when new relations are inferred.

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References

  1. James F. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832–843, 1983.

    Google Scholar 

  2. Silvana Badaloni and Marina Berati. Hybrid temporal reasoning for planning and scheduling. In TIME-96: Proc. of the 3 rd Int. Workshop on Temporal Representation and Reasoning, Los Alamitos, CA, 1996. IEEE Computer Society Press.

    Google Scholar 

  3. Eliseo Clementini, Paolino Di Felice, and Daniel Hernández. Qualitative representation of positional information. Artificial Intelligence, 95:317–356, 1997.

    Article  Google Scholar 

  4. Ernest Davis. Constraint propagation with interval labels. Artificial Intelligence, 32:281–332, 1987.

    Article  Google Scholar 

  5. Rina Dechter, Itay Meiri, and Judea Pearl. Temporal constraint networks. Artificial Intelligence, 49(1-3):61–95, 1991.

    Article  MathSciNet  Google Scholar 

  6. James Foley, Andrew van Dam, Steven Feiner, and John Hughes. Computer Graphics: Principles and Practice. Addison-Wesley, Reading, MA, 1996.

    Google Scholar 

  7. Christian Freksa. Temporal reasoning based on semi-intervals. Artificial Intelligence, 54(1–2):199–227, 1992.

    Article  Google Scholar 

  8. Daniel Hernández, Eliseo Clementini, and Paolino Di Felice. Qualitative distances. In A. U. Frank, editor, Spatial Information Theory: A Theoretical Basis for GIS, number 988 in LNCS, pages 45–56, Berlin, 1995. Springer.

    Google Scholar 

  9. Jerry R. Hobbs. Granularity. In IJCAI-85: Proc. of the 9 th Int. Joint Conference on Artificial Intelligence, pages 432–435, Los Altos, CA, 1985. Morgan Kaufmann.

    Google Scholar 

  10. Henry A. Kautz and Peter B. Ladkin. Integrating metric and qualitative temporal reasoning. In AAAI-91: Proc. of the 9th National Conf. on Artificial Intelligence, pages 241–246, Menlo Park, CA, Cambridge, MA, 1991. AAAI Press; MIT Press.

    Google Scholar 

  11. Itay Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Artificial Intelligence, 87:343–385, 1996.

    Article  Google Scholar 

  12. Eddie Schwalb and Rina Dechter. Processing disjunctions in temporal constraint networks. Artificial Intelligence, 93:29–61, 1997.

    Article  Google Scholar 

  13. Steffen Staab and Udo Hahn. “Tall”, “good”, “high” — Compared to what? In IJCAI-97.Proc. of the 15th International Joint Conference on Artificial Intelligence, pages 996–1001, San Francisco, CA, 1997. Morgan Kaufmann.

    Google Scholar 

  14. Marc Vilain, Henry Kautz, and Peter van Beek. Constraint propagation algorithms for temporal reasoning: A revised report. In Daniel S. Weld and Johan de Kleer, editors, Readings in Qualitative Reasoning about Physics, pages 373–381. Morgan Kaufmann, San Mateo, CA, 1989.

    Google Scholar 

  15. Kai Zimmermann. Measuring without measures. The Δ-calculus. In A. U. Frank, editor, Spatial Information Theory: A Theoretical Basis for GIS, number 988 in LNCS, pages 59–67, Berlin, 1995. Springer.

    Google Scholar 

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Robert E. Mercer Eric Neufeld

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© 1998 Springer-Verlag Berlin Heidelberg

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Staab, S., Hahn, U. (1998). Distance constraint arrays: A model for reasoning on intervals with qualitative and quantitative distances. In: Mercer, R.E., Neufeld, E. (eds) Advances in Artificial Intelligence. Canadian AI 1998. Lecture Notes in Computer Science, vol 1418. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64575-6_62

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  • DOI: https://doi.org/10.1007/3-540-64575-6_62

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64575-7

  • Online ISBN: 978-3-540-69349-9

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