Abstract
Various forms of commonsense reasoning may be used to cope with situations where insufficient knowledge is available for a given purpose. In this paper, we rely on such a strategy to complete sets of symbolic categorization rules, starting from background information about the semantic relationship of different properties and concepts. Our solution is based on Gärdenfors conceptual spaces, which allow us to express semantic relationships with a geometric flavor. In particular, we take the inherently qualitative notion of betweenness as primitive, and show how it naturally leads to patterns of interpolative reasoning. Both a semantic and a syntactic characterization of this process is presented, and the computational complexity is analyzed. Finally, some patterns of extrapolative reasoning are sketched, based on the notions of betweenness and parallelism.
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References
Billen, R., Clementini, E.: Semantics of collinearity among regions. In: Chung, S., Herrero, P. (eds.) OTM-WS 2005. LNCS, vol. 3762, pp. 1066–1076. Springer, Heidelberg (2005)
Collins, A., Michalski, R.: The logic of plausible reasoning: A core theory. Cognitive Science 13(1), 1–49 (1989)
Dubois, D., Prade, H., Esteva, F., Garcia, P., Godo, L.: A logical approach to interpolation based on similarity relations. International Journal of Approximate Reasoning 17(1), 1–36 (1997)
Dupin de Saint-Cyr, F., Lang, J.: Belief extrapolation (or how to reason about observations and unpredicted change). Artif. Intell. 175(2), 760–790 (2011)
Forbus, K.D.: Qualitative process theory. Artif. Intell. 24(1-3), 85–168 (1984)
Gärdenfors, P.: Conceptual Spaces: The Geometry of Thought. MIT Press, Cambridge (2000)
Gardenfors, P., Williams, M.: Reasoning about categories in conceptual spaces. In: Int. Joint Conf. on Artificial Intelligence, pp. 385–392 (2001)
Gérard, R., Kaci, S., Prade, H.: Ranking alternatives on the basis of generic constraints and examples: a possibilistic approach. In: International Joint Conference on Artifical Intelligence, pp. 393–398 (2007)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1-2), 167–207 (1990)
Kuipers, B.: Qualitative simulation. Artificial Intelligence 29(3), 289–338 (1986)
Lehmann, F., Cohn, A.G.: The EGG/YOLK reliability hierarchy: semantic data integration using sorts with prototypes. In: Int. Conf. on Information and Knowledge Management, pp. 272–279 (1994)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1992)
Prade, H., Schockaert, S.: Completing rule bases in symbolic domains by analogy making. In: 7th Conf. of the European Society for Fuzzy Logic and Technology (2011)
Roy, B.: The outranking approach and the foundations of ELECTRE methods. Theory and Decision 31, 49–73 (1991)
Ruspini, E.: On the semantics of fuzzy logic. International Journal of Approximate Reasoning 5, 45–88 (1991)
Schockaert, S., Prade, H.: An inconsistency-tolerant approach to information merging based on proposition relaxation. In: AAAI Conf. on Artificial Intelligence, pp. 363–368 (2010)
Schockaert, S., Prade, H.: Interpolation and extrapolation in conceptual spaces: A case study in the music domain. In: Proceedings of the 5th International Conference on Web Reasoning and Rule Systems (2011)
Sun, R.: Robust reasoning: integrating rule-based and similarity-based reasoning. Artificial Intelligence 75(2), 241–295 (1995)
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Schockaert, S., Prade, H. (2011). Qualitative Reasoning about Incomplete Categorization Rules Based on Interpolation and Extrapolation in Conceptual Spaces. In: Benferhat, S., Grant, J. (eds) Scalable Uncertainty Management. SUM 2011. Lecture Notes in Computer Science(), vol 6929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23963-2_24
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DOI: https://doi.org/10.1007/978-3-642-23963-2_24
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