Related papers: Categorical Calculus and Algebra for Multi-Model D…
One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human.…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
Many classification problems require decisions among a large number of competing classes. These tasks, however, are not handled well by general purpose learning methods and are usually addressed in an ad-hoc fashion. We suggest a general…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
Language-integrated query based on comprehension syntax is a powerful technique for safe database programming, and provides a basis for advanced techniques such as query shredding or query flattening that allow efficient programming with…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
The usefulness of annotated corpora is greatly increased if there is an associated tool that can allow various kinds of operations to be performed in a simple way. Different kinds of annotation frameworks and many query languages for them…
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…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
We develop a novel framework that aims to create bridges between the computational social choice and the database management communities. This framework enriches the tasks currently supported in computational social choice with relational…
The Data Web refers to the vast and rapidly increasing quantity of scientific, corporate, government and crowd-sourced data published in the form of Linked Open Data, which encourages the uniform representation of heterogeneous data items…
For complex data types such as multimedia, traditional data management methods are not suitable. Instead of attribute matching approaches, access methods based on object similarity are becoming popular. Recently, this resulted in an…
Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL.…
We develop a multiset query and update language executable in a term rewriting system. Its most remarkable feature, besides non-standard approach to quantification and introduction of fresh values, is non-determinism - a query result is not…
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…
This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra…
We address a fundamental question concerning spatio-temporal database systems: ``What are exactly spatio-temporal queries?'' We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a…