Related papers: Data Base Mappings and Theory of Sketches
This paper proposes a categorical framework for knowledge graphs linking combinatorial graph structure with topos-theoretic semantics. Knowledge graphs are represented as labelled directed multigraphs and analysed through incidence matrices…
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…
It is increasingly common to find complex data represented through the graph model. Contrary to relational models, graphs offer a high capacity for executing analytical tasks on complex data. Since a huge amount of data is still presented…
In the recent years, a lot of attention has been paid to the development of solid foundations for the composition and inversion of schema mappings. In this paper, we review the proposals for the semantics of these crucial operators. For…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…
In Text-to-SQL semantic parsing, selecting the correct entities (tables and columns) for the generated SQL query is both crucial and challenging; the parser is required to connect the natural language (NL) question and the SQL query to the…
Based on the previously proposed concept Understanding Tree, this paper introduces two concepts: Understanding Graph and Understanding Map, and explores their potential applications. Understanding Graph and Understanding Map can be deemed…
A graph is a structure composed of a set of vertices (i.e.nodes, dots) connected to one another by a set of edges (i.e.links, lines). The concept of a graph has been around since the late 19$^\text{th}$ century, however, only in recent…
In mathematics education research, mathematics task sets involving mixed practice include tasks from many different topics within the same assignment. In this paper, we use graph decompositions to construct mixed practice task sets for…
In this paper, we motivated the need for relational database systems to support subset query processing. We defined new operators in relational algebra, and new constructs in SQL for expressing subset queries. We also illustrated the…
Modeling data lineage in relational databases remains a challenging problem, particularly in scenarios involving incomplete or missing dependencies between database objects. In this paper, we propose a novel ontology for relational database…
Cryptography is a theory of secret functions. Category theory is a general theory of functions. Cryptography has reached a stage where its structures often take several pages to define, and its formulas sometimes run from page to page.…
Data warehouses are nowadays an important component in every competitive system, it's one of the main components on which business intelligence is based. We can even say that many companies are climbing to the next level and use a set of…
We survey foundational features underlying modern graph query languages. We first discuss two popular graph data models: edge-labelled graphs, where nodes are connected by directed, labelled edges; and property graphs, where nodes and edges…
We present in this article the model Function-described graph (FDG), which is a type of compact representation of a set of attributed graphs (AGs) that borrow from Random Graphs the capability of probabilistic modelling of structural and…
Property graphs have reached a high level of maturity, witnessed by multiple robust graph database systems as well as the ongoing ISO standardization effort aiming at creating a new standard Graph Query Language (GQL). Yet, despite…
Transferring latent structure from one environment or problem to another is a mechanism by which humans and animals generalize with very little data. Inspired by cognitive and neurobiological insights, we propose graph schemas as a…
A theory of sketches for arithmetic universes (AUs) is developed. A restricted notion of sketch, called here "context", is defined with the property that every non-strict model is uniquely isomorphic to a strict model. This allows us to…
Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL.…
Motivated by the need to extract knowledge and value from interconnected data, graph analytics on big data is a very active area of research in both industry and academia. To support graph analytics efficiently a large number of in memory…