Related papers: Data Base Mappings and Monads: (Co)Induction
We present a categorical denotational semantics for a database mapping, based on views, in the most general framework of a database integration/exchange. Developed database category DB, for databases (objects) and view-based mappings…
Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures…
In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This…
The graph database (GDB) is an increasingly common storage model for data involving relationships between entries. Beyond its widespread usage in database industries, the advantages of GDBs indicate a strong potential in constructing…
Ontology-based data access (OBDA) is a popular approach for integrating and querying multiple data sources by means of a shared ontology. The ontology is linked to the sources using mappings, which assign views over the data to ontology…
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…
The category $\mathbf{Rel}$ is the category of sets (objects) and relations (morphisms). Equipped with the direct product of sets, $\mathbf{Rel}$ is a monoidal category. Moreover, $\mathbf{Rel}$ is a locally posetal 2-category, since every…
The aim of the paper is to build a connection between two approaches towards categorical language theory: the coalgebraic and algebraic language theory for monads. For a pair of monads modelling the branching and the linear type we defined…
We use monads to relax the atomicity requirement for data in a database. Depending on the choice of monad, the database fields may contain generalized values such as lists or sets of values, or they may contain exceptions such as various…
We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints…
In this paper, we define a category DB, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps. Along the way we give a precise formulation of the category of relational…
Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a…
In this paper, we address the problem of learning low dimension representation of entities on relational databases consisting of multiple tables. Embeddings help to capture semantics encoded in the database and can be used in a variety of…
Recent work on database application development platforms has sought to include a declarative formulation of a conceptual data model in the application code, using annotations or attributes. Some recent work has used metadata to include the…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
We address the problem of learning a distributed representation of entities in a relational database using a low-dimensional embedding. Low-dimensional embeddings aim to encapsulate a concise vector representation for an underlying dataset…
In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database…
Most of data on the Web are still stored in relational databases. Therefore, it is more important to make the correspondence between relational databases (RDB) and ontologies for storing the Web data. In this paper, we present an new…
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…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…