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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Authors
- 1. Guillermo Badia (University of Queensland)
- 2. Phokion G. Kolaitis (IBM; University of California Santa Cruz)
- 3. Carles Noguera (University of Siena)
BibTeX Citation
@inproceedings{badia_pods26,
address = {New York, NY, USA},
series = {{PODS} '26},
title = {{Codd's Theorem for Databases over Semirings}},
url = {https://dl.acm.org/doi/10.1145/3767713},
doi = {10.1145/3767713},
booktitle = {Proceedings of the {ACM} {SIGMOD} Symposium on {Principles} of {Database} {Systems}},
publisher = {Association for Computing Machinery},
author = {Badia, Guillermo and Kolaitis, Phokion G. and Noguera, Carles},
year = {2026}
}
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Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 17 | Provenance Semirings | 2007 | PODS | 0.00059843817 |
| 2,600 | Convergence of Datalog over (Pre-) Semirings | 2022 | PODS | 8.3571843e-05 |
| 6,301 | Evaluating Datalog over Semirings: A Grounding-based Approach | 2024 | PODS | 5.9213518e-05 |
| 11,136 | Consistency of Relations over Monoids | 2024 | PODS | 5.093636e-05 |
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