Abstract
A central notion in qualitative spatial and temporal reasoning is the concept of qualitative constraint calculus, which captures a particular paradigm of representing and reasoning about spatial and temporal knowledge. The concept, informally used in the research community for a long time, was formally defined by Ligozat and Renz in 2004 as a special kind of relation algebra — thus emphasizing a particular type of reasoning about binary constraints. Although the concept is known to be limited it has prevailed in the community. In this paper we revisit the concept, contrast it with alternative approaches, and analyze general properties. Our results indicate that the concept of qualitative constraint calculus is both too narrow and too general: it disallows different approaches, but its setup already enables arbitrarily hard problems.
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References
Ligozat, G., Renz, J.: What is a qualitative calculus? A general framework. In: Zhang, C., Guesgen, H.W., Yeap, W.K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 53–64. Springer, Heidelberg (2004)
Ligozat, G.: Categorical methods in qualitative reasoning: The case for weak representations. In: Cohn, A.G., Mark, D.M. (eds.) COSIT 2005. LNCS, vol. 3693, pp. 265–282. Springer, Heidelberg (2005)
Dylla, F., Mossakowski, T., Schneider, T., Wolter, D.: Algebraic properties of qualitative spatio-temporal calculi. In: Tenbrink, T., Stell, J., Galton, A., Wood, Z. (eds.) COSIT 2013. LNCS, vol. 8116, pp. 516–536. Springer, Heidelberg (2013)
Bodirsky, M.: Constraint satisfaction problems with infinite templates. In: Creignou, N., Kolaitis, P.G., Vollmer, H. (eds.) Complexity of Constraints. LNCS, vol. 5250, pp. 196–228. Springer, Heidelberg (2008)
Bodirsky, M., Dalmau, V.: Datalog and constraint satisfaction with infinite templates. Journal of Computer and System Sciences 79(1), 79–100 (2013)
Bodirsky, M., Chen, H.: Qualitative temporal and spatial reasoning revisited. Journal of Logic and Computation 19(6), 1359–1383 (2009)
Hodges, W.: Model Theory. Encyclopedia of Mathematics and its Applications. Cambridge University Press (1993)
Maddux, R.: Some varieties containing relation algebras. Transactions of the American Mathematical Society 272(2) (1982)
Hirsch, R., Hodkinson, I.M.: Step by step - building representations in algebraic logic. The Journal of Symbolic Logic 62(1), 225–279 (1997)
Hodkinson, I.M.: Atom structures of relation algebras (1995), retrieved from his homepage: http://www.doc.ic.ac.uk/~imh/
Mackworth, A.K., Freuder, E.C.: The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artificial Intelligence 25(1), 65–74 (1985)
Renz, J., Ligozat, G.: Weak composition for qualitative spatial and temporal reasoning. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 534–548. Springer, Heidelberg (2005)
Bauslaugh, B.L.: The complexity of infinite h-coloring. Journal of Combinatorial Theory, Series B 61(2), 141–154 (1994)
Bodirsky, M., Wölfl, S.: RCC8 is polynomial on networks of bounded treewidth. In: Walsh, T. (ed.) IJCAI, pp. 756–761. IJCAI/AAAI (2011)
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Westphal, M., Hué, J., Wölfl, S. (2014). On the Scope of Qualitative Constraint Calculi. In: Lutz, C., Thielscher, M. (eds) KI 2014: Advances in Artificial Intelligence. KI 2014. Lecture Notes in Computer Science(), vol 8736. Springer, Cham. https://doi.org/10.1007/978-3-319-11206-0_20
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DOI: https://doi.org/10.1007/978-3-319-11206-0_20
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