2,255 research outputs found
The State-of-the-Art of Set Visualization
Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net
Accessible reasoning with diagrams: From cognition to automation
High-tech systems are ubiquitous and often safety and se- curity critical: reasoning about their correctness is paramount. Thus, precise modelling and formal reasoning are necessary in order to convey knowledge unambiguously and accurately. Whilst mathematical mod- elling adds great rigour, it is opaque to many stakeholders which leads to errors in data handling, delays in product release, for example. This is a major motivation for the development of diagrammatic approaches to formalisation and reasoning about models of knowledge. In this paper, we present an interactive theorem prover, called iCon, for a highly expressive diagrammatic logic that is capable of modelling OWL 2 ontologies and, thus, has practical relevance. Significantly, this work is the first to design diagrammatic inference rules using insights into what humans find accessible. Specifically, we conducted an experiment about relative cognitive benefits of primitive (small step) and derived (big step) inferences, and use the results to guide the implementation of inference rules in iCon
A cognitive exploration of the “non-visual” nature of geometric proofs
Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as
a way to explore the similarities and differences between diagrams and text (visual
thinking versus language thinking). Traditional text-based proofs are considered
(by many to be) more rigorous than diagrams alone. In this paper we focus on
human perceptual-cognitive characteristics that may encourage textual modes for
proofs because of the ergonomic affordances of text relative to diagrams. We suggest
that visual-spatial perception of physical objects, where an object is perceived
with greater acuity through foveal vision rather than peripheral vision, is similar
to attention navigating a conceptual visual-spatial structure. We suggest that attention
has foveal-like and peripheral-like characteristics and that textual modes
appeal to what we refer to here as foveal-focal attention, an extension of prior
work in focused attention
Learning with multiple representations: An example of a revision lesson in mechanics
We describe an example of learning with multiple representations in an
A-level revision lesson on mechanics. The context of the problem involved the
motion of a ball thrown vertically upwards in air and studying how the
associated physical quantities changed during its flight. Different groups of
students were assigned to look at the ball's motion using various
representations: motion diagrams, vector diagrams, free-body diagrams, verbal
description, equations and graphs, drawn against time as well as against
displacement. Overall, feedback from students about the lesson was positive. We
further discuss the benefits of using computer simulation to support and extend
student learning.Comment: 10 pages, 5 figures, 2 tables http://iopscience.iop.org/0031-912
Human inference beyond syllogisms: an approach using external graphical representations.
Research in psychology about reasoning has often been restricted to relatively inexpressive statements involving quantifiers (e.g. syllogisms). This is limited to situations that typically do not arise in practical settings, like ontology engineering. In order to provide an analysis of inference, we focus on reasoning tasks presented in external graphic representations where statements correspond to those involving multiple quantifiers and unary and binary relations. Our experiment measured participants' performance when reasoning with two notations. The first notation used topological constraints to convey information via node-link diagrams (i.e. graphs). The second used topological and spatial constraints to convey information (Euler diagrams with additional graph-like syntax). We found that topo-spatial representations were more effective for inferences than topological representations alone. Reasoning with statements involving multiple quantifiers was harder than reasoning with single quantifiers in topological representations, but not in topo-spatial representations. These findings are compared to those in sentential reasoning tasks
PaL Diagrams: A Linear Diagram-Based Visual Language
Linear diagrams have recently been shown to be
more effective than Euler diagrams when used
for set-based reasoning. However, unlike the
growing corpus of knowledge about formal aspects
of Euler and Venn diagrams, there has been no
formalisation of linear diagrams. To fill this
knowledge gap, we present and formalise Point
and Line (PaL) diagrams, an extension of simple
linear diagrams containing points, thus providing
a formal foundation for an effective visual
language.We prove that PaL diagrams are exactly
as expressive as monadic first-order logic with
equality, gaining, as a corollary, an equivalence
with the Euler diagram extension called spider
diagrams. The method of proof provides translations
between PaL diagrams and sentences of monadic
first-order logic
Proceedings of the Graduate Student Symposium of the 7th International Conference on the Theory and Application of Diagrams, July 5 2012
Proceedings of the Graduate Student Symposium held at the 7th International Conference on the Theory and Application of Diagrams, ( Diagrams 2012 ), held at the University of Kent on July 5, 2012. Dr. Nathaniel Miller, professor of in the School of Mathematical Sciences at UNC, served on the symposium organizing committee
- …