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Databases have been studied category-theoretically for decades. The database schema -- whose purpose is to arrange high-level conceptual entities -- is generally modeled as a category or sketch. The data itself, often called an instance, is…

Category Theory · Mathematics 2025-01-20 Patrick Schultz , David I. Spivak , Christina Vasilakopoulou , Ryan Wisnesky

Nested conditions are used, among other things, as a graphical way to express first order formulas ruling the applicability of a graph transformation rule to a given match. In this paper, we propose (for the first time) a notion of…

Logic in Computer Science · Computer Science 2024-08-13 Arend Rensink , Andrea Corradini

In data exchange, data are materialised from a source schema to a target schema, according to suitable source-to-target constraints. Constraints are also expressed on the target schema to represent the domain of interest. A schema mapping…

Databases · Computer Science 2014-01-03 Andrea Calì , Riccardo Torlone

We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…

Logic in Computer Science · Computer Science 2021-07-07 Dennis Peuter , Philipp Marohn , Viorica Sofronie-Stokkermans

It is known that the composition of schema mappings, each specified by source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO tgd). We consider the question of what happens when target constraints are allowed.…

Databases · Computer Science 2015-07-01 Marcelo Arenas , Ronald Fagin , Alan Nash

The technique of \emph{equality saturation}, which equips graphs with an equivalence relation, has proven effective for program optimisation. We give a categorical semantics to these structures, called \emph{e-graphs}, in terms of Cartesian…

Logic in Computer Science · Computer Science 2025-05-21 Aleksei Tiurin , Chris Barrett , Dan R. Ghica , Nick Hu

Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of a shared ontology. The ontology is linked to the sources using mappings, which assign views over the data to ontology…

Artificial Intelligence · Computer Science 2017-05-22 Charalampos Nikolaou , Egor V. Kostylev , George Konstantinidis , Mark Kaminski , Bernardo Cuenca Grau , Ian Horrocks

Recent standardization work for database languages has reflected the growing use of typed graph models (TGM) in application development. Such data models are frequently only used early in the design process, and not reflected directly in…

Databases · Computer Science 2024-07-10 Malcolm Crowe , Fritz Laux

We propose a novel framework to facilitate the on-demand design of data-centric systems by exploiting domain knowledge from an existing ontology. Its key ingredient is a process that we call focusing, which allows to obtain a schema for a…

Logic in Computer Science · Computer Science 2019-04-02 Tomasz Gogacz , Víctor Gutiérrez-Basulto , Yazmín A. Ibáñez-García , Filip Murlak , Magdalena Ortiz , Mantas Šimkus

We consider database schemas consisting of a single binary relation, with key constraints and inclusion dependencies. Over this space of 20 schemas, we completely characterize when one schema is generically dominated by another schema.…

Databases · Computer Science 2026-03-19 Benoît Groz , Jan Hidders , Nina Pardal , Jan Van den Bussche , Piotr Wieczorek

Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema…

Databases · Computer Science 2022-01-14 Valter Uotila , Jiaheng Lu

A 0-1 matrix $M$ contains a 0-1 matrix pattern $P$ if we can obtain $P$ from $M$ by deleting rows and/or columns and turning arbitrary 1-entries into 0s. The saturation function $\mathrm{sat}(P,n)$ for a 0-1 matrix pattern $P$ indicates the…

Combinatorics · Mathematics 2023-09-28 Benjamin Aram Berendsohn

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be…

Databases · Computer Science 2012-01-04 Shuai Ma , Yang Cao , Wenfei Fan , Jinpeng Huai , Tianyu Wo

Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…

Programming Languages · Computer Science 2024-02-14 Alex Dixon , Andrzej S. Murawski

Equality saturation, a technique for program optimisation and reasoning, has gained attention due to the resurgence of equality graphs (e-graphs). E-graphs represent equivalence classes of terms under rewrite rules, enabling simultaneous…

Logic in Computer Science · Computer Science 2025-05-05 Aleksei Tiurin , Dan R. Ghica , Nick Hu

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of…

Computational Complexity · Computer Science 2009-02-10 Andrei A. Bulatov , Victor Dalmau , Martin Grohe , Daniel Marx

Ontology-based data integration has been one of the practical methodologies for heterogeneous legacy database integrated service construction. However, it is neither efficient nor economical to build the cross-domain ontology on top of the…

Databases · Computer Science 2021-03-16 Yuanwei Zhao , Lan Huang , Bo Wang , Dongxu Zhang , Simone Bocca , Fausto Giunchiglia , Rui Zhang

An applied problem facing all areas of data science is harmonizing data sources. Joining data from multiple origins with unmapped and only partially overlapping features is a prerequisite to developing and testing robust, generalizable…

Previous work has demonstrated that categories are useful and expressive models for databases. In the present paper we build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern…

Category Theory · Mathematics 2019-02-20 David I. Spivak

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original…

Databases · Computer Science 2021-10-20 Leopoldo Bertossi