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)
Incoming Non-self Citations Over Time
No non-self incoming citations found for this paper in this database.
Authors
Incoming Citations (Sorted by Pagerank)
Showing 0 of 0 citing papers.
| Rank | Citing Paper | Year | Venue | Pagerank |
|---|
Previous
Page 1 / 1
Next
Outgoing Citations (Sorted by Pagerank)
Showing 4 of 4 cited papers.
Citations counted here include only citations to other VLDB/SIGMOD/CIDR/PODS papers in this database.
| Rank | Cited Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 31 | Provenance Semirings | 2007 | PODS | 0.00078516827 |
| 2,912 | Convergence of Datalog over (Pre-) Semirings | 2022 | PODS | 7.9261665e-05 |
| 5,996 | Evaluating Datalog over Semirings: A Grounding-based Approach | 2024 | PODS | 5.2365238e-05 |
| 10,919 | Consistency of Relations over Monoids | 2024 | PODS | 4.1905499e-05 |
Previous
Page 1 / 1
Next
Semantically Similar Papers
| Overall Rank | Paper | Year | Venue | Pagerank |
|---|---|---|---|---|
| 8,256 | Counting Problems over Incomplete Databases | 2020 | PODS | 4.5440379e-05 |
| 7,722 | On the complexity of division and set joins in the relational algebra | 2005 | PODS | 4.6628934e-05 |
| 2,808 | On the Expressive Power of Database Queries with Intermediate Types | 1988 | PODS | 8.0939851e-05 |
| 2,097 | Axiomatic Foundations and Algorithms for Deciding Semantic Equivalences of SQL Queries | 2018 | VLDB | 9.5439744e-05 |
| 4,343 | Languages for Relational Databases over Interpreted Structures | 1997 | PODS | 6.2665123e-05 |
| 453 | The Theory Of Probabilistic Databases | 1987 | VLDB | 0.00022801484 |
| 3,195 | On Accessing Object-Oriented Databases: Expressive Power, Complexity, and Restrictions | 1989 | SIGMOD | 7.4052272e-05 |
| 31 | Provenance Semirings | 2007 | PODS | 0.00078516827 |
| 13,049 | Relational Algebras, Logic, And Functional Programming | 1984 | SIGMOD | 4.1905499e-05 |
| 1,450 | Theory of Database Queries (Extended Abstract) | 1988 | PODS | 0.00011926567 |