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Computing Logic Programming Semantics in Linear Algebra

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Multi-disciplinary Trends in Artificial Intelligence (MIWAI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11248))

Abstract

Logic programming is a logic-based programming paradigm, and provides languages for declarative problem solving and symbolic reasoning. In this paper, we develop new algorithms for computing logic programming semantics in linear algebra. We first introduce an algorithm for computing the least model of a definite logic program using matrices. Next, we introduce an algorithm for computing stable models of a normal logic program. We also develop optimization techniques for speeding-up those algorithms. Finally, the complexity of them is analyzed and tested in practice.

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Notes

  1. 1.

    In [8], the fact is represented by \( ^{{{\prime \prime }}} p_{i} \leftarrow {\sf T}^{{{\prime \prime }}} \) and is encoded in a matrix by aij = 1 where \( {\text{row}}_{i} \left( {M_{P} } \right) = p_{i} \;{\text{and}}\;{\text{col}}_{j} \left( {M_{P} } \right) = {\sf T}. \):

  2. 2.

    A definite program P satisfies the MD-condition if it satisfies the following condition: For any two rules r1 and r2 in P (r1 ≠ r2): head(r1) = head(r2) implies |body(r1)| ≤1 and |body(r2)| ≤ 1.

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Acknowledgment

This work was supported by JSPS KAKENHI Grant Numbers JP17H00763 and JP18H03288.

Author information

Authors and Affiliations

  1. University of Information Technology, VNU-HCM, Ho Chi Minh City, Vietnam

    Hien D. Nguyen

  2. Wakayama University, Wakayama, Japan

    Chiaki Sakama

  3. AI Research Center AIST, Tokyo, Japan

    Taisuke Sato

  4. National Institute of Informatics (NII), Tokyo, Japan

    Katsumi Inoue

Authors
  1. Hien D. Nguyen
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  2. Chiaki Sakama
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  3. Taisuke Sato
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  4. Katsumi Inoue
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Corresponding author

Correspondence to Hien D. Nguyen .

Editor information

Editors and Affiliations

  1. Mahasarakham University, Maha Sarakham, Thailand

    Manasawee Kaenampornpan

  2. Center for Computing Technologies, University of Bremen, Bremen, Germany

    Rainer Malaka

  3. Vietnam Academy of Science and Technology, Hanoi, Vietnam

    Duc Dung Nguyen

  4. AIST Tokyo, Tokyo, Japan

    Nicolas Schwind

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Nguyen, H.D., Sakama, C., Sato, T., Inoue, K. (2018). Computing Logic Programming Semantics in Linear Algebra. In: Kaenampornpan, M., Malaka, R., Nguyen, D., Schwind, N. (eds) Multi-disciplinary Trends in Artificial Intelligence. MIWAI 2018. Lecture Notes in Computer Science(), vol 11248. Springer, Cham. https://doi.org/10.1007/978-3-030-03014-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-03014-8_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03013-1

  • Online ISBN: 978-3-030-03014-8

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