Abstract
In most knowledge representation settings, atomic properties correspond to natural language labels. Although these labels are usually taken to be primitive, automating some forms of commonsense inference requires background knowledge on the cognitive meaning of these labels. We consider two such forms of commonsense reasoning, which we refer to as interpolative and extrapolative reasoning. In both cases, rule-based knowledge is augmented with knowledge about the geometric representation of labels in a conceptual space. Specifically, to support interpolative reasoning, we need to know which labels are conceptually between which other labels, considering that intermediary conditions tend to lead to intermediary conclusions. Extrapolative reasoning is based on information about the direction of change that is needed when replacing one label by another, taking the view that parallel changes in the conditions of rules tend to lead to parallel changes in the conclusions. In this paper, we propose a practical method to acquire such knowledge about the conceptual spaces representation of labels. We illustrate the method in the domain of music genres, starting from meta-data that was obtained from the music recommendation website last.fm.
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References
Bouchon-Meunier, B., Esteva, F., Godo, L., Rifqi, M., Sandri, S.: A principled approach to fuzzy rule base interpolation using similarity relations. In: Proc. of the EUSFLAT-LFA Joint Conference, Barcelona, pp. 757–763
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., Jeansoulin, R., Prade, H.: Spatial information fusion: Coping with uncertainty in conceptual structures. In: ICCS Supplement, pp. 66–74 (2008)
Dupin de Saint-Cyr, F., Lang, J.: Belief extrapolation (or how to reason about observations and unpredicted change). Artificial Intelligence 175(2), 760–790 (2011)
Gärdenfors, P.: Conceptual Spaces: The Geometry of Thought. MIT Press, Cambridge (2000)
Gardenfors, P., Williams, M.: Reasoning about categories in conceptual spaces. In: International Joint Conference 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: Int. Joint Conf. on Artifical intelligence, pp. 393–398 (2007)
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)
Miclet, L., Prade, H.: Handling analogical proportions in classical logic and fuzzy logics settings. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 638–650. Springer, Heidelberg (2009)
Prade, H., Richard, G.: Reasoning with logical proportions. In: International Conference on Principles of Knowledge Representation and Reasoning (KR), pp. 545–555 (2010)
Ruspini, E.: On the semantics of fuzzy logic. International Journal of Approximate Reasoning 5, 45–88 (1991)
Schockaert, S., Prade, H.: Qualitative reasoning about incomplete categorization rules based on interpolation and extrapolation in conceptual spaces. In: Proceedings of the Fifth International Conference on Scalable Uncertainty Management (2011)
Schockaert, S., Prade, H.: Solving conflicts in information merging by a flexible interpretation of atomic propositions. Artificial Intelligence 175, 1815–1855 (2011)
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Schockaert, S., Prade, H. (2011). Interpolation and Extrapolation in Conceptual Spaces: A Case Study in the Music Domain. In: Rudolph, S., Gutierrez, C. (eds) Web Reasoning and Rule Systems. RR 2011. Lecture Notes in Computer Science, vol 6902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23580-1_16
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DOI: https://doi.org/10.1007/978-3-642-23580-1_16
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