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Logic programming in tensor spaces

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Abstract

This paper introduces a novel approach to computing logic programming semantics. First, a propositional Herbrand base is represented in a vector space and if-then rules in a program are encoded in a matrix. Then the least fixpoint of a definite logic program is computed by matrix-vector products with a non-linear operation. Second, disjunctive logic programs are represented in third-order tensors and their minimal models are computed by algebraic manipulation of tensors. Third, normal logic programs are represented by matrices and third-order tensors, and their stable models are computed. The result of this paper exploits a new connection between linear algebraic computation and symbolic computation, which has the potential to realize logical inference in huge scale of knowledge bases.

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Acknowledgments

We thank the reviewers for valuable comments. This work is supported by JSPS KAKENHI Grant Number JP18H03288.

Funding

This work is supported by JSPS KAKENHI Grant Number JP18H03288

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Authors and Affiliations

  1. Wakayama University, 930 Sakaedani, Wakayama, 640 8510, Japan

    Chiaki Sakama

  2. National Institute of Informatics, Tokyo, Japan

    Katsumi Inoue & Taisuke Sato

Authors
  1. Chiaki Sakama
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  2. Katsumi Inoue
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  3. Taisuke Sato
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Contributions

All authors contributed to the study conception and formulation. The first draft of the manuscript was written by the first author and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Chiaki Sakama.

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Sakama, C., Inoue, K. & Sato, T. Logic programming in tensor spaces. Ann Math Artif Intell 89, 1133–1153 (2021). https://doi.org/10.1007/s10472-021-09767-x

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