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Abductive Logic Programming and Linear Algebraic Computation

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Handbook of Abductive Cognition

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Abstract

Abduction has been applied to various problems in many fields, and computing abductive explanations is an essential task in such applications. Logic programming has been used for both representation languages and computational procedures for abductive computation. This chapter summarizes the novel approach to use linear algebra for abduction in logic programming developed by the authors. The method is built on top of the fixed-point computation of matrix-vector multiplications for deduction in logic programming, where a matrix and vectors, respectively, represent a logic program and interpretations. For abduction, a similar technique is employed for multiplications of an abductive matrix and observation vectors, together with enumeration of minimal hitting sets by avoiding dimension explosion. Compared with logical methods based on symbolic manipulation, the linear algebraic method has an advantage for efficient computation.

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Acknowledgements

This work has been supported by JSPS KAKENHI Grant Numbers JP18H03288 and JP21H04905, and by JST CREST Grant Number JPMJCR22D3, Japan.

Tuan Nguyen Quoc has also been supported by Monbukagakusho (MEXT) Scholarship and Japan International Cooperative Agency “Innovative Asia”.

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Authors and Affiliations

  1. The Graduate University for Advanced Studies, SOKENDAI, Japan

    Tuan Quoc Nguyen & Katsumi Inoue

  2. National Institute of Informatics, Tokyo, Japan

    Tuan Quoc Nguyen & Katsumi Inoue

  3. Wakayama University, Wakayama, Japan

    Chiaki Sakama

Authors
  1. Tuan Quoc Nguyen
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  2. Katsumi Inoue
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  3. Chiaki Sakama
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Corresponding author

Correspondence to Katsumi Inoue .

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Editors and Affiliations

  1. Department of Humanities, University of Pavia, Pavia, Italy

    Lorenzo Magnani

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Nguyen, T.Q., Inoue, K., Sakama, C. (2023). Abductive Logic Programming and Linear Algebraic Computation. In: Magnani, L. (eds) Handbook of Abductive Cognition. Springer, Cham. https://doi.org/10.1007/978-3-031-10135-9_62

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