Related papers: Algebraic Data Integration
Data comes in many forms. From a shallow perspective, they can be viewed as being either in structured (e.g., as a relation, as key-value pairs) or unstructured (e.g., text, image) formats. So far, machines have been fairly good at…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…
This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…
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…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
We report on implementing graph grammars for intelligence analysis in OCaml. Graph grammars are represented as elements of an algebraic data type in OCaml. In addition to algebraic data types, we use other concepts from functional…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
In spatial databases, incompatibilities often arise due to different choices of origin or unit of measurement (e.g., centimeters versus inches). By representing and querying the data in an affine-invariant manner, we can avoid these…
Integrating various data modalities brings valuable insights into underlying phenomena. Multimodal factor analysis (FA) uncovers shared axes of variation underlying different simple data modalities, where each sample is represented by a…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…
Companies and individuals produce numerous tabular data. The objective of this position paper is to draw up the challenges posed by the automatic integration of data in the form of tables so that they can be cross-analyzed. We provide a…
This paper continues the discussion of the representation and interpretation of ontologies in the first-order logical environment {\ttfamily FOLE} (Kent). Ontologies are represented and interpreted in (many-sorted) first-order logic. Five…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
Context graphs are essential for modern AI applications including question answering, pattern discovery, and data analysis. Building accurate context graphs from structured databases requires inferring join relationships between entities.…
Message Sequence Charts & Sequence Diagrams are graphical models that represent the behavior of distributed and concurrent systems via the scheduling of discrete and local emission and reception events. We propose an Interaction Language…
This paper introduces annotative indexing, a novel framework that unifies and generalizes traditional inverted indexes, column stores, object stores, and graph databases. As a result, annotative indexing can provide the underlying indexing…
Most modern applications interact with external services and access data in structured formats such as XML, JSON and CSV. Static type systems do not understand such formats, often making data access more cumbersome. Should we give up and…