Related papers: Data Base Mappings and Monads: (Co)Induction
The logic of nulls in databases has been subject of investigation since their introduction in Codd's Relational Model, which is the foundation of the SQL standard. We show a logical characterisation of a first-order fragment of SQL with…
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…
Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model…
This paper defines a constraint-based model dedicated to multidimensional databases. The model we define represents data through a constellation of facts (subjects of analyse) associated to dimensions (axis of analyse), which are possibly…
Deep learning models heavily rely on large scale annotated datasets for training. Unfortunately, datasets cannot capture the infinite variability of the real world, thus neural networks are inherently limited by the restricted visual and…
We introduce a contravariant idempotent adjunction between (i) the category of ranked monads on $\mathsf{Set}$; and (ii) the category of internal categories and internal retrofunctors in the category of locales. The left adjoint takes a…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
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…
It is well established that equational algebraic theories, and the monads they generate, can be used to encode computational effects. An important insight of Power and Shkaravska is that comodels of an algebraic theory T -- i.e., models in…
Relational knowledge bases (KBs) are commonly used to represent world knowledge in machines. However, while advantageous for their high degree of precision and interpretability, KBs are usually organized according to manually-defined…
Many web databases can be seen as providing partial and overlapping information about entities in the world. To answer queries effectively, we need to integrate the information about the individual entities that are fragmented over multiple…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
We propose Cognitive Databases, an approach for transparently enabling Artificial Intelligence (AI) capabilities in relational databases. A novel aspect of our design is to first view the structured data source as meaningful unstructured…
In this paper we introduce the SchemaDB data-set; a collection of relational database schemata in both sql and graph formats. Databases are not commonly shared publicly for reasons of privacy and security, so schemata are not available for…
Relational databases (RDBs) contain vast amounts of heterogeneous tabular information that can be exploited for predictive modeling purposes. But since the space of potential targets is vast across enterprise settings, how can we…
This paper overviews an approach that addresses machine learning over relational data as a database problem. This is justified by two observations. First, the input to the learning task is commonly the result of a feature extraction query…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
We consider the setting of a Semantic Web database, containing both explicit data encoded in RDF triples, and implicit data, implied by the RDF semantics. Based on a query workload, we address the problem of selecting a set of views to be…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
In the current paper, we propose to fuse together stored data (tables) and their functional dependencies (FDs) inside a DBMS. We aim to make FDs first-class citizens: objects which can be queried and used to query data. Our idea is to allow…