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For decades, SQL has been the default language for composing queries, but it is increasingly used as an artifact to be read and verified rather than authored. With Large Language Models (LLMs), queries are increasingly machine-generated,…
The increasing rise in artificial intelligence has made the use of imprecise language in computer programs like ChatGPT more prominent. Fuzzy logic addresses this form of imprecise language by introducing the concept of fuzzy sets, where…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Language-integrated query is a powerful programming construct allowing database queries and ordinary program code to interoperate seamlessly and safely. Language-integrated query techniques rely on classical results about the nested…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…
A significant category of NoSQL approaches is known as graph da-tabases. They are usually represented by one property graph. We introduce a functional approach to modelling relations and property graphs. Single-valued and multivalued…
Many works have focused, for over twenty five years, on the integration of the time dimension in databases (DB). However, the standard SQL3 does not yet allow easy definition, manipulation and querying of temporal DBs. In this paper, we…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
Students in introductory data management courses are often taught how to write queries in SQL. This is a useful and practical skill, but it gives limited insight into how queries are processed by relational database engines. In contrast,…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those…
The relational data model was designed to facilitate large-scale data management and analytics. We consider the problem of how to differentiate computations expressed relationally. We show experimentally that a relational engine running an…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database…
The task of generating a database query from a question in natural language suffers from ambiguity and insufficiently precise description of the goal. The problem is amplified when the system needs to generalize to databases unseen at…
The Web of Linked Data is composed of tons of RDF documents interlinked to each other forming a huge repository of distributed semantic data. Effectively querying this distributed data source is an important open problem in the Semantic Web…
Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…