Abstract.
Logical and analogical reasoning are sometimes viewed as mutually exclusive alternatives, but formal logic is actually a highly constrained and stylized method of using analogies. Before any subject can be formalized to the stage where logic can be applied to it, analogies must be used to derive an abstract representation from a mass of irrelevant detail. After the formalization is complete, every logical step – of deduction, induction, or abduction – involves the application of some version of analogy. This paper analyzes the relationships between logical and analogical reasoning, and describes a highly efficient analogy engine that uses conceptual graphs as the knowledge representation. The same operations used to process analogies can be combined with Peirce’s rules of inference to support an inference engine. Those operations, called the canonical formation rules for conceptual graphs, are widely used in CG systems for language understanding and scene recognition as well as analogy finding and theorem proving. The same algorithms used to optimize analogy finding can be used to speed up all the methods of reasoning based on the canonical formation rules.
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References
Chalmers, D.J., French, R.M., Hofstadter, D.R.: High-level perception, representation, and analogy: A critique of artificial intelligence methodology. Journal of Experimental & Theoretical Artificial Intelligence 4, 185–211 (1992)
Falkenhainer, B., Forbus, K.D., Gentner, D.: The Structure mapping engine: algorithm and examples. Artificial Intelligence 41, 1–63 (1989)
Forbus, K.D., Gentner, D., Law, K.: MAC/FAC: A Model of Similarity-Based Retrieval. Cognitive Science 19(2), 141–205 (1995)
Forbus, K.D., Gentner, D., Markman, A.B., Ferguson, R.W.: Analogy just looks like high level perception: Why a domain-general approach to analogical mapping is right. Journal of Experimental & Theoretical Artificial Intelligence 10(2), 231–257 (1998)
Forbus, K.D., Mostek, T., Ferguson, R.: An analogy ontology for integrating analogical processing and first-principles reasoning. In: Proc. IAAI-2002 pp. 878–885 (2002)
Gentzen, G.: Untersuchungen über das logische Schließen, translated as Investigations into logical deduction. In: Szabo, M.E. (ed.) The Collected Papers of Gerhard Gentzen, pp. 68–131. North-Holland Publishing Co., Amsterdam (1935)
Hallaq, W.B.: Ibn Taymiyya Against the Greek Logicians. Clarendon Press, Oxford (1993)
LeClerc, A., Majumdar, A.: Legacy revaluation and the making of LegacyWorks. Distributed Enterprise Architecture 5(9), Cutter Consortium, Arlington, MA (2002)
Morrison, C.T., Dietrich, E.: Structure-mapping vs. high-level perception: the mistaken fight over the explanation of Analogy. In: Proc. 17th Annual Conference of the Cognitive Science Society, pp. 678–682 (1995), Available at http://babs.cs.umass.edu/clayton/CogSci95/SM-v-HLP.html
Peirce, C.S.: Logical machines. American Journal of Psychology 1, 165–170 (1887)
Peirce, C.S.: Logic, Considered as Semeiotic. In: Ransdell, J. (ed.) MS L75 (1902), http://members.door.net/arisbe/menu/LIBRARY/bycsp/L75/ver1/l75v1-01.htm
Peirce, C.S.: Manuscript 514, with commentary by J. F. Sowa (1909), available at http://www.jfsowa.com/peirce/ms514.htm
Sowa, J.F.: Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks/Cole Publishing Co, Pacific Grove (2000)
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Sowa, J.F., Majumdar, A.K. (2003). Analogical Reasoning. In: Ganter, B., de Moor, A., Lex, W. (eds) Conceptual Structures for Knowledge Creation and Communication. ICCS 2003. Lecture Notes in Computer Science(), vol 2746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45091-7_2
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DOI: https://doi.org/10.1007/978-3-540-45091-7_2
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