On matrices and K -relations

We show that the matrix query language M A T L A N G 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 M A T L A N G 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.