Related papers: Theory is Shapes
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. We formally investigate Euler diagrams as an…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Belief systems are often treated as globally consistent sets of propositions or as scalar-valued probability distributions. Such representations tend to obscure the internal structure of belief, conflate external credibility with internal…
This article combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these…
Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are…
The construction of an ontology of scientific knowledge objects, presented here, is part of the development of an approach oriented towards the visualization of scientific knowledge. It is motivated by the fact that the concepts that are…
Probabilistic models inform an increasingly broad range of business and policy decisions ultimately made by people. Recent algorithmic, computational, and software framework development progress facilitate the proliferation of Bayesian…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for specifying and reasoning about algorithms that manipulate mathematical…
Figures visually represent an essential piece of information and provide an effective means to communicate scientific facts. Recently there have been many efforts toward extracting data directly from figures, specifically from tables,…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
Graphics (e.g., figures and charts) are ubiquitous in scientific papers, yet separating graphics from text increases cognitive load in understanding text-graphic connections. Research has found that word-scale graphics, or visual…
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
Bayesian data analysis is about more than just computing a posterior distribution, and Bayesian visualization is about more than trace plots of Markov chains. Practical Bayesian data analysis, like all data analysis, is an iterative process…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
Stories are records of our experiences and their analysis reveals insights into the nature of being human. Successful analyses are often interdisciplinary, leveraging mathematical tools to extract structure from stories and insights from…
The basic objective of data visualization is to provide an efficient graphical display for summarizing and reasoning about quantitative information. During the last decades, political science has accumulated a large corpus of various kinds…
Natural language and visualization are being increasingly deployed together for supporting data analysis in different ways, from multimodal interaction to enriched data summaries and insights. Yet, researchers still lack systematic…
Conceptual Graphs (CG) are a graph-based knowledge representation and reasoning formalism; fuzzy Conceptual Graphs (fCG) constitute an extension that enriches their expressiveness, exploiting the fuzzy set theory so as to relax their…