Representing Knowledge and Querying Data using Double-Functorial Semantics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916967790673920 |
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| author | Lambert, Michael Patterson, Evan |
| author_facet | Lambert, Michael Patterson, Evan |
| contents | Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the 2-category of sets, relations, and implications. The functional and relational models are unified by double functors into the double category of sets, functions, relations, and implications. In an accessible, example-driven style, we show that the abstract structure of a 'double category of relations' is a flexible and expressive language in which to represent knowledge, and we show how queries on data in the spirit of Codd's relational algebra are captured by double-functorial semantics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Representing Knowledge and Querying Data using Double-Functorial Semantics Lambert, Michael Patterson, Evan Category Theory Databases Logic in Computer Science Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the 2-category of sets, relations, and implications. The functional and relational models are unified by double functors into the double category of sets, functions, relations, and implications. In an accessible, example-driven style, we show that the abstract structure of a 'double category of relations' is a flexible and expressive language in which to represent knowledge, and we show how queries on data in the spirit of Codd's relational algebra are captured by double-functorial semantics. |
| title | Representing Knowledge and Querying Data using Double-Functorial Semantics |
| topic | Category Theory Databases Logic in Computer Science |
| url | https://arxiv.org/abs/2403.19884 |