Abstract
Classical deduction is limited as a tool for reasoning about logical domain theories, in its ability to make sense of situations that are not explicitly covered. Humans on the other hand are remarkably adept at speculation about new situations, by drawing analogies or by relying on knowledge of similar situations. In this chapter, we are interested in formalising this process to develop a form of commonsense reasoning about incomplete rule bases. More precisely, we discuss two methods which can be used to derive plausible rules from a given set of propositional rules and a set of analogical proportions. The first method is based on the view that whenever the antecedents of four rules are in an analogical proportion, their consequences are likely to be in an analogical proportion as well. It often produces useful results, although it may be too adventurous for some applications. The second method is more cautious and makes explicit the assumptions under which it produces sound conclusions. Finally, we show how the second method may be further refined, in such a way that we recover the first method as a special case.
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References
Carnap, R.: A basic system of inductive logic, part 2. In: Studies in Inductive Logic and Probability, vol. 2, pp. 7–155. University of California Press, Berkeley (1980)
Dubois, D., Esteva, F., Godo, L., Prade, H.: An information-based discussion of vagueness. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, vol. 2, pp. 781–784 (2001)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.N.D., Hogger, C., Robinson, J. (ed.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)
Fine, K.: Vagueness, truth and logic. Synthese 30(3), 265–300 (1975)
Furnas, G.W., Deerwester, S., Dumais, S.T., Landauer, T.K., Harshman, R.A., Streeter, L.A., Lochbaum, K.E.: Information retrieval using a singular value decomposition model of latent semantic structure. In: Proceedings of the 11th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 465–480 (1988)
Gabrilovich, E. Markovitch, S.: Computing semantic relatedness using wikipedia-based explicit semantic analysis. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, vol. 6, pp. 1606–1611 (2007)
Gärdenfors, P.: Conceptual Spaces: The Geometry of Thought. MIT Press, Cambridge (2000)
Gärdenfors, P., Williams, M.: Reasoning about categories in conceptual spaces. In: International Joint Conference on Artificial Intelligence, pp. 385–392 (2001)
Kern-Isberner, G., Fisseler, J.: Knowledge discovery by reversing inductive knowledge representation. In: Proceedings of the 9th International Conference on Principles of Knowledge Representation and Reasoning, pp. 34–44 (2004)
Lakoff, G.: Hedges: a study in meaning criteria and the logic of fuzzy concepts. J. Philoso. Logic 2(4), 458–508 (1973)
Lawry, J., Tang, Y.: Uncertainty modelling for vague concepts: a prototype theory approach. Artif. Intell. 173(18), 1539–1558 (2009)
Losos, J.B.: Phylogenetic niche conservatism, phylogenetic signal and the relationship between phylogenetic relatedness and ecological similarity among species. Ecol. Lett. 11(10), 995–1003 (2008)
Miclet, L., Prade, H.: Handling analogical proportions in classical logic and fuzzy logics settings. In: Sossai, C., Chemello, G. (ed.) European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 638–650 (2009)
Prade, H., Richard, G.: Multiple-valued logic interpretations of analogical, reverse analogical, and paralogical proportions. In: Proceedings of the 40th IEEE International Symposium on Multiple-Valued Logic, pp. 258–263 (2010)
Prade, H., Richard, G.: Reasoning with logical proportions. In: Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning, pp. 545–555 (2010)
Prade H., Richard, G.: Analogical proportions and multiple-valued logics. In: van der Gaag, L.C. (ed.) Proceedings of the 12th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, vol. 7958, pp. 497–509 (2013)
Prade, H., Schockaert, S.: Completing rule bases in symbolic domains by analogy making. In: Proceedings of the EUSFLAT-LFA Conference, pp. 928–934 (2011)
Rosch, E.H.: Natural categories. Cogn. Psychol. 4(3), 328–350 (1973)
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, pp. 217–231 (2011)
Schockaert, S., Prade, H.: Solving conflicts in information merging by a flexible interpretation of atomic propositions. Artif. Intell. 175(11), 1815–1855 (2011)
Schockaert, S., Prade, H.: Cautious analogical-proportion based reasoning using qualitative conceptual relations. In: Proceedings of the ECAI 2012 Workshop on Similarity and Analogy-Based Methods in AI, pp. 41–48 (2012)
Schockaert, S., Prade, H.: Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces. Artif. Intell. 202, 86–131 (2013)
Speer, R., Havasi, C., Lieberman, H.: Analogyspace: reducing the dimensionality of common sense knowledge. In: Proceedings of the 23rd AAAI Conference on Artificial intelligence, pp. 548–553 (2008)
Sun, R.: Robust reasoning: integrating rule-based and similarity-based reasoning. Artif. Intell. 75(2), 241–295 (1995)
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The authors are indebted to the two reviewers for their useful comments about the presentation of the ideas.
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Schockaert, S., Prade, H. (2014). Completing Symbolic Rule Bases Using Betweenness and Analogical Proportion. In: Prade, H., Richard, G. (eds) Computational Approaches to Analogical Reasoning: Current Trends. Studies in Computational Intelligence, vol 548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54516-0_8
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