Related papers: Alg\`ebre OLAP et langage graphique
This paper combines the classical model of labeled transition systems with the epistemic model for reasoning about knowledge. The result is a unifying framework for modeling and analyzing multi-agent, knowledge-based, dynamic systems. On…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
Answer set programming (ASP) is a popular nonmonotonic-logic based paradigm for knowledge representation and solving combinatorial problems. Computing the answer set of an ASP program is NP-hard in general, and researchers have been…
Recent findings in neuroscience suggest that the human brain represents information in a geometric structure (for instance, through conceptual spaces). In order to communicate, we flatten the complex representation of entities and their…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
This paper introduces SGL, a graphics language that is aesthetically similar to SQL. As a graphical counterpart to SQL, SGL enables specification of statistical graphics within SQL query interfaces. SGL is based on a grammar of graphics…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Data processing systems roughly group into families such as relational, array, graph, and key-value. Many data processing tasks exceed the capabilities of any one family, require data stored across families, or run faster when partitioned…
We describe a new approach to data modeling, called the concept-oriented model (COM), and a novel concept-oriented query language (COQL). The model is based on three principles: duality principle postulates that any element is a couple…
Human reasoning in visual analytics of data networks relies mainly on the quality of visual perception and the capability of interactively exploring the data from different facets. Visual quality strongly depends on networks' size and…
Data quality assessment and data cleaning are context-dependent activities. Motivated by this observation, we propose the Ontological Multidimensional Data Model (OMD model), which can be used to model and represent contexts as logic-based…
The paper is devoted to showing how to systematically design a programming language in 'reverse order', i.e. from denotations to syntax. This construction is developed in an algebraic framework consisting of three many-sorted algebras: of…
This paper uses typed linear algebra (LA) to represent data and perform analytical querying in a single, unified framework. The typed approach offers strong type checking (as in modern programming languages) and a diagrammatic way of…
To exploit the Web Ontology Language OWL as an answer set programming (ASP) language, we introduce the notion of bounded model semantics, as an intuitive and computationally advantageous alternative to its classical semantics. We show that…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
In this paper we describe a new approach to data modelling called the concept-oriented model (CoM). This model is based on the formalism of nested ordered sets which uses inclusion relation to produce hierarchical structure of sets and…
Class algebra provides a natural framework for sharing of ISA hierarchies between users that may be unaware of each other's definitions. This permits data from relational databases, object-oriented databases, and tagged XML documents to be…
In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of…