Abstract
Reasoning about complex dependencies between events is a crucial task. However, qualitative reasoning has so far concentrated on spatial and temporal issues. In contrast, we present a new dependency calculus (DC) that is created for specific questions of reasoning about causal relations and consequences. Applications in the field of spatial representation and reasoning are, for instance, modeling traffic networks, ecological systems, medical diagnostics, and Bayesian Networks. Several extensions of the fundamental linear point algebra have been investigated, for instance on trees or on nonlinear structures. DC is an improved generalization that meets all requirements to describe dependencies on networks. We investigate this structure with respect to satisfiability problems, construction problems, tractable subclassses, and embeddings into other relation algebras. Finally, we analyze the associated interval algebra on network structures.
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References
Allen, J.F.: Maintaining knowledge about temporal intervals. Comm. ACM 26(11), 832–843 (1983)
Anger, F., Ladkin, P., Rodriguez, R.: Atomic temporal interval relations in branching time: Calculation and application. In: Actes 9th SPIE Conference on Applications of AI, Orlando, FL, USA (1991)
Broxvall, M., Jonsson, P.: Towards a complete classification of tractability in point algebras for nonlinear time. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 129–143. Springer, Heidelberg (1999)
Broxvall, M., Jonsson, P., Renz, J.: Refinements and Independence: A Simple Method for Identifying Tractable Disjunctive Constraints. In: CP, pp. 114–127 (2000)
Cohn, A.G.: Qualitative spatial representation and reasoning techniques. In: Brewka, G., Habel, C., Nebel, B. (eds.) KI 1997. LNCS (LNAI), vol. 1303, pp. 1–30. Springer, Heidelberg (1997)
Drakengren, T., Jonsson, P.: A complete classification of tractability in Allen’s algebra relative to subsets of basic relations. Artificial Intelligence 106(2), 205–219 (1998)
Freksa, C.: Using Orientation Information for Qualitative Spatial Reasoning. In: Frank, A.U., Campari, I., Formentini, U. (eds.) Theories and Methods of Spatial-Temporal in Geographic Space, pp. 162–178 (1992)
Ladkin, P.B., Maddux, R.D.: On binary constraint problems. J. ACM (1994)
Montanari, U.: Networks of constraints: Fundamental properties and applications to picture processing. Inform. Sci. 7, 95–132 (1974)
Nebel, B., Bürckert, H.-J.: Reasoning about temporal relations: A maximal tractable subclass of Allen’s interval algebra. J. ACM 42(1), 43–66 (1995)
Randell, D., Cui, Z., Cohn, A.: A Spatial Logic Based on Regions and Connection. In: Proceedings KR-1992, pp. 165–176 (1992)
Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the Region Connection Calculus. AIJ 108(1-2), 69–123 (1999)
Renz, J.: A Spatial Odyssey of the Interval Algebra: 1. Directed Intervals. In: Proc. of IJCAI 2001 (2001)
Vilain, M.B., Kautz, H.A., van Beek, P.G.: Contraint propagation algorithms for temporal reasoning: A revised report. Reasoning about Physical Systems, 373–381 (1989)
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Ragni, M., Scivos, A. (2005). Dependency Calculus: Reasoning in a General Point Relation Algebra. In: Furbach, U. (eds) KI 2005: Advances in Artificial Intelligence. KI 2005. Lecture Notes in Computer Science(), vol 3698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11551263_6
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DOI: https://doi.org/10.1007/11551263_6
Publisher Name: Springer, Berlin, Heidelberg
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