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arXiv · 2611.08474

Monus vs. Interpretations in Semiring Semantics

Phokion G. Kolaitis
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Abstract

Interpretations have been widely used in the study of provenance of queries on semiring-annotated databases. Here, we consider two different interpretation-based semantics for first-order formulas in negation normal form, namely, the canonical-interpretation semantics and the compatible-interpretation semantics. We show that the resulting query languages cannot express the monus operation on semiring-annotated relations, when the annotations come from the bag semiring or the tropical semiring or the fuzzy semiring. Consequently, the semantics of SQL cannot be captured using the interpretation-based semantics considered here.

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Phokion G. Kolaitis. 2026-11-05. Monus vs. Interpretations in Semiring Semantics. https://arxiv.org/abs/2611.08474

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