Codd's Theorem for Databases over Semirings
Summary: Extends Codd's theorem to semiring-annotated databases, proving algebra–calculus equivalence in two variants: one for the five basic ops and one for five ops plus division. Models difference via semirings-with-monus and shows division may be inexpressible from the five ops over positive semirings (e.g., bags, tropical). (summarized by gpt-5-mini on Feb 11 2026)
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| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 31 | Provenance Semirings | 2007 | PODS | 0.0007857786 |
| 2,907 | Convergence of Datalog over (Pre-) Semirings | 2022 | PODS | 7.933806e-05 |
| 5,992 | Evaluating Datalog over Semirings: A Grounding-based Approach | 2024 | PODS | 5.2415551e-05 |
| 10,915 | Consistency of Relations over Monoids | 2024 | PODS | 4.1945683e-05 |
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