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Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation,…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
In this paper we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory. In our formalism, database schemas and instances are algebraic (multi-sorted…
A significant number of novel database architectures and data models have been proposed during the last decade. While some of these new systems have gained in popularity, they lack a proper formalization, and a precise understanding of the…
There exists a wide set of techniques to perform keyword-based search over relational databases but all of them match the keywords in the users' queries to elements of the databases to be queried as first step. The matching process is a…
A common approach to data analysis involves understanding and manipulating succinct representations of data. In earlier work, we put forward a succinct representation system for relational data called factorised databases and reported on…
We propose the vision of a functional data model (FDM) and an associated functional query language (FQL). Our proposal has far-reaching consequences: we show a path to come up with a modern QL that solves (almost if not) all problems of SQL…
Existing query languages for data discovery exhibit system-driven designs that emphasize database features and functionality over user needs. We propose a re-prioritization of the client through an introduction of a language-driven approach…
We propose a new approach to querying graph databases. Our approach balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
Data analysis often involves comparing subsets of data across many dimensions for finding unusual trends and patterns. While the comparison between subsets of data can be expressed using SQL, they tend to be complex to write, and suffer…
This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of…
We describe a new approach to data modeling, called the concept-oriented model (COM), and a novel concept-oriented query language (COQL). The model is based on three principles: duality principle postulates that any element is a couple…
In this paper, we present the case for a declarative foundation for data-intensive machine learning systems. Instead of creating a new system for each specific flavor of machine learning task, or hardcoding new optimizations, we argue for…
Querying and exploring massive collections of data sources, such as data lakes, has been an essential research topic in the database community. Although many efforts have been paid in the field of data discovery and data integration in data…
Recent advances in tabular question answering (QA) with large language models are constrained in their coverage and only answer questions over a single table. However, real-world queries are complex in nature, often over multiple tables in…
The purpose of predictive modeling on relational data is to predict future or missing values in a relational database, for example, future purchases of a user, risk of readmission of the patient, or the likelihood that a financial…
We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic:…
Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…
Tables have gained significant attention in large language models (LLMs) and multimodal large language models (MLLMs) due to their complex and flexible structure. Unlike linear text inputs, tables are two-dimensional, encompassing formats…