Enhancing Linear Algebraic Computation of Logic Programs Using Sparse Representation

Tuan Nguyen Quoc, Katsumi Inoue, and Chiaki Sakama

Proceedings 36th International Conference on Logic Programming (Technical Communications) (ICLP 2020), UNICAL, Rende (CS), Italy, 18-24th September 2020, Electronic Proceedings in Theoretical Computer Science 325, pages 192-205.


Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference in large scale knowledge bases. This paper proposes further improvement by using sparse matrices to embed logic programs in vector spaces. We show its great power of computation in reaching the fixpoint of the immediate consequence operator from the initial vector. In particular, performance for computing the least models of definite programs is dramatically improved in this way. We also apply the method to the computation of stable models of normal programs, in which the guesses are associated with initial matrices, and verify its effect when there are small numbers of negation. These results show good enhancement in terms of performance for computing consequences of programs and depict the potential power of tensorized logic programs.

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