We show that the matrix query language 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 2. We then proceed to show that MATLANG can express all matrix queries expressible in the positive relational algebra on K-relations, when intermediate arities are restricted to 3. 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.

中文翻译：

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关于矩阵和 K 关系

我们证明矩阵查询语言M A T L A N G对应于K关系上的正关系代数的自然片段。该片段是通过引入组合运算符并将K关系数限制为 2 来定义的。然后我们继续证明M A T L A N G可以表达所有可在K上的正关系代数中表达的矩阵查询-关系，当中间数被限制为 3 时。因此，我们在具有数值数据的模型中提供了经典逻辑中的情况的类比，其中二元关系的代数等效于具有三个变量的一阶逻辑。