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Abduction as Incomplete Parameter Estimation
1  Faculty of Science and Technology, Tokyo University of Science

Abstract: Abduction, which is a kind of inference, is clearly articulated by C.S. Peirce (Peirce 1868; 1955). Although abduction is considered as reasoning with uncertainty (Finlay and Dix, 1996), it has been studied in artificial intelligence and computer science (Bylander et al 1991; Abe 2003). Recently, constructing a dynamical model which represents logical inferences, Sawa and Gunji use an arrow diagram which represents three types of inference articulated by Peirce (i.e. deduction, induction and abduction). This formalization for abduction is not only consistent with the preceding studies (Peirce 1868; Finlay and Dix 1996), but also opens up the way by which abduction can be applied to numerical function systems (Kamiura 2010). In this paper, based on the Sawa-Gunji's inference diagram, a numerical aspect of abduction is formalized as incomplete parameter estimation.
Keywords: Abduction, Parameter estimation, Inference, Power law