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.

中文翻译：

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使用稀疏表示增强逻辑程序的线性代数计算

近年来，逻辑程序的代数表征受到越来越多的关注。研究人员试图利用线性代数计算和符号计算之间的联系，以便在大规模知识库中执行逻辑推理。本文提出了通过使用稀疏矩阵在向量空间中嵌入逻辑程序的进一步改进。我们展示了从初始向量到达直接后果算子的固定点的强大计算能力。特别是，计算确定程序的最少模型的性能以这种方式显着提高。我们还将该方法应用于正常程序的稳定模型的计算，其中猜测与初始矩阵相关联，并在存在少量否定时验证其效果。