Abstract
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.
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Acknowledgements
We thank Floris Geerts for inspiring discussions.
We also thank the anonymous reviewers for their comments which were very helpful in improving this paper.
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This is a revised and extended version of the conference paper “On matrices and K-relations” presented at the 11th International Symposium on Foundations of Information and Knowledge Systems (FoIKS 2020), Dortmund, Germany, February 17–21, 2020 [5].
Robert Brijder has done this work as a Postdoctoral Fellow of the Research Foundation – Flanders (FWO).
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Brijder, R., Gyssens, M. & Van den Bussche, J. On matrices and K-relations. Ann Math Artif Intell 90, 181–210 (2022). https://doi.org/10.1007/s10472-021-09760-4
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DOI: https://doi.org/10.1007/s10472-021-09760-4