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Linear Algebraic Abduction with Partial Evaluation

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Practical Aspects of Declarative Languages (PADL 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13880))

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Abstract

Linear algebra is an ideal tool to redefine symbolic methods with the goal to achieve better scalability. In solving the abductive Horn propositional problem, the transpose of a program matrix has been exploited to develop an efficient exhaustive method. While it is competitive with other symbolic methods, there is much room for improvement in practice. In this paper, we propose to optimize the linear algebraic method for abduction using partial evaluation. This improvement considerably reduces the number of iterations in the main loop of the previous algorithm. Therefore, it improves practical performance especially with sparse representation in case there are multiple subgraphs of conjunctive conditions that can be computed in advance. The positive effect of partial evaluation has been confirmed using artificial benchmarks and real Failure Modes and Effects Analysis (FMEA)-based datasets.

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Notes

  1. 1.

    This behavior is unlike the behavior of the previous definition in [22] that we set 0 at the diagonal that will eliminate all values of Or-rule head atoms in \(v_0\).

  2. 2.

    We excluded the unresolved problem .

  3. 3.

    A PAR-2 score of a solver is defined as the sum of all runtimes for solved instances plus 2 times timeout for each unsolved instance.

  4. 4.

    https://github.com/pysathq/pysat.

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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.

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Authors and Affiliations

  1. National Institute of Informatics, Tokyo, Japan

    Tuan Nguyen & Katsumi Inoue

  2. Wakayama University, Wakayama, Japan

    Chiaki Sakama

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

Correspondence to Tuan Nguyen , Katsumi Inoue or Chiaki Sakama .

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Editors and Affiliations

  1. University of Kiel, Kiel, Germany

    Michael Hanus

  2. Miami University, Oxford, OH, USA

    Daniela Inclezan

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Nguyen, T., Inoue, K., Sakama, C. (2023). Linear Algebraic Abduction with Partial Evaluation. In: Hanus, M., Inclezan, D. (eds) Practical Aspects of Declarative Languages. PADL 2023. Lecture Notes in Computer Science, vol 13880. Springer, Cham. https://doi.org/10.1007/978-3-031-24841-2_13

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  • DOI: https://doi.org/10.1007/978-3-031-24841-2_13

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  • Online ISBN: 978-3-031-24841-2

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