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arXiv · 1904.03934

On matrices and $K$-relations

Robert Brijder·Marc Gyssens·Jan Van den Bussche
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Abstract

We show that the matrix query language $\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation arities to two. We then proceed to show that $\mathsf{MATLANG}$ can express all matrix queries expressible in the positive relational algebra on $K$-relations, when intermediate arities are restricted to three. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to first-order logic with three variables.

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Robert Brijder, Marc Gyssens, Jan Van den Bussche. 2019-04-08. On matrices and $K$-relations. https://arxiv.org/abs/1904.03934

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