Related papers: Functorial Data Migration
A Datalog program can be viewed as a syntactic specification of a functor from database instances over some schema to database instances over another schema. The same holds more generally for $\exists$Datalog. We establish large classes of…
We develop a rigorous, equation-free category-theoretic foundation for fungal organisation. A fungal organism is formalised as a functor from a category $\Env$ of structured environmental states and admissible transformations to a category…
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, arrays, vectors, and matrices. We developed SDQL, a statically…
Large enterprise databases can be complex and messy, obscuring the data semantics needed for analytical tasks. We propose a semantic layer in-between the database and the user as a set of small and easy-to-interpret database views,…
Text-to-SQL is emerging as a practical interface for real world databases. The dominant paradigm for Text-to-SQL is cross-database or schema-independent, supporting application schemas unseen during training. The schema of a database…
The article suggests a description of a system of tables with a set of special lists absorbing a semantics of data and reflects a fullness of data. It shows how their parallel processing can be constructed based on the descriptions. The…
This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…
Modern database systems face a significant challenge in effectively handling the Variety of data. The primary objective of this paper is to establish a unified data model and theoretical framework for multi-model data management. To achieve…
We introduce functorial language models: a principled way to compute probability distributions over word sequences given a monoidal functor from grammar to meaning. This yields a method for training categorical compositional distributional…
There are increasingly efficient data processing pipelines that work on vectors of numbers, for instance most machine learning models, or vector databases for fast similarity search. These require converting the data to numbers. While this…
Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the…
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…
Database schema elements such as tables, views, triggers and functions are typically defined with many interrelationships. In order to support database users in understanding a given schema, a rule-based approach for analyzing the…
This paper is about Kripke structures that are inside a relational database and queried with a modal language. At first the modal language that is used is introduced, followed by a definition of the database and relational algebra. Based on…
We present a general methodology for structuring textual data, represented as syntax trees enriched with semantic information, guided by a meta-model G defined as an attribute grammar. The method involves an evolution process where both the…
Parallel transport of a connection in a smooth fibre bundle yields a functor from the path groupoid of the base manifold into a category that describes the fibres of the bundle. We characterize functors obtained like this by two notions we…
Conventional database architectures often secure local consistency by discarding information, entangling correctness with loss. We introduce the Functorial-Categorical Database (FCDb), which models data operations as morphisms in a layered…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…