相关论文: Matching, Merging and Structural Properties of Dat…
In this paper we will present the two basic operations for database schemas used in database mapping systems (separation and Data Federation), and we will explain why the functorial semantics for database mappings needed a new base category…
We present an index structure to boost the evaluation of free-connex acyclic conjunctive queries (fc-ACQs) over relational databases. The main ingredient of the index associated with a given database $D$ is an auxiliary database $D_{col}$.…
This paper rigorously and concisely defines, in the context of our (Elementary) Mathematical Data Model ((E)MDM), the mathematical concepts of dyadic relation, reflexivity, irreflexivity, symmetry, asymmetry, transitivity, intransitivity,…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
A database driven web application is a very common software solution to rising business problems. Modeling the database and the software architecture can be challenging, hence there not being one combined modeling language for database and…
Although researchers have devoted considerable attention to helping database users formulate queries, many users still find it challenging to specify queries that involve joining tables. To help users construct join queries for exploring…
Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical…
In the past few years, the number of OLAP applications increased quickly. These applications use two significantly different DB structures: multidimensional (MD) and table-based. One can show that the traditional model of relational…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
This is the first of a pair of papers where we construct and investigate a closed monoidal structure on the category of generalized algebraic theories (in the sense of Cartmell). In the present text, as a starting point, we define the…
A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…
Querying is one of the basic functionality expected from a database system. Query efficiency is adversely affected by increase in the number of participating tables. Also, querying based on syntax largely limits the gamut of queries a…
Matching Dependencies (MDs) are a relatively recent proposal for declarative entity resolution. They are rules that specify, given the similarities satisfied by values in a database, what values should be considered duplicates, and have to…
In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this…
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…
A number of domain specific languages, such as circuits or data-science workflows, are best expressed as diagrams of boxes connected by wires. Unfortunately, functional languages have traditionally been ill-equipped to embed this sort of…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…
The paper is devoted to a categorical study of the category of probabilistic metric spaces. The study is based on an isomorphic description of the category of probabilistic metric spaces. The isomorphic description was obtained in [3] and…
We discuss several useful interpretations of the categorical dimension of objects in a braided fusion category, as well as some conjectures demonstrating the value of quantum dimension as a quantum statistic for detecting certain behaviors…