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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)

Paper ID
2054
Venue
PODS
Year
2026
Pagerank
5.093636e-05
Overall Rank
10,177 | 30.18%
DOI
10.1145/3767713

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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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