On the Completeness of Spider Diagrams Augmented with Constants

Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable

Evaluation of the usability of constraint diagrams as a visual modelling language: theoretical and empirical investigations

This research evaluates the constraint diagrams (CD) notation, which is a formal representation for program specification that has some promise to be used by people who are not expert in software design. Multiple methods were adopted in order to provide triangulated evidence of the potential benefits of constraint diagrams compared with other notational systems. Three main approaches were adopted for this research. The first approach was a semantic and task analysis of the CD notation. This was conducted by the application of the Cognitive Dimensions framework, which was used to examine the relative strengths and weaknesses of constraint diagrams and conventional notations in terms of the perceptive facilitation or impediments of these different representations. From this systematic analysis, we found that CD cognitively reduced the cost of exploratory design, modification, incrementation, searching, and transcription activities with regard to the cognitive dimensions: consistency, visibility, abstraction, closeness of mapping, secondary notation, premature commitment, role-expressiveness, progressive evaluation, diffuseness, provisionality, hidden dependency, viscosity, hard mental operations, and error-proneness. The second approach was an empirical evaluation of the comprehension of CD compared to natural language (NL) with computer science students. This experiment took the form of a web-based competition in which 33 participants were given instructions and training on either CD or the equivalent NL specification expressions, and then after each example, they responded to three multiple-choice questions requiring the interpretation of expressions in their particular notation. Although the CD group spent more time on the training and had less confidence, they obtained comparable interpretation scores to the NL group and took less time to answer the questions, although they had no prior experience of CD notation. The third approach was an experiment on the construction of CD. 20 participants were given instructions and training on either CD or the equivalent NL specification expressions, and then after each example, they responded to three questions requiring the construction of expressions in their particular notation. We built an editor to allow the construction of the two notations, which automatically logged their interactions. In general, for constructing program specification, the CD group had more accurate answers, they had spent less time in training, and their returns to the training examples were fewer than those of the NL group. Overall it was found that CD is understandable, usable, intuitive, and expressive with unambiguous semantic notation

Euler diagram-based notations

Euler diagrams have been used for centuries as a means for conveying logical statements in a simple, intuitive way. They form the basis of many diagrammatic notations used to represent set-theoretic relationships in a wide range of contexts including software modelling, logical reasoning systems, statistical data representation, database search queries and file system management. In this paper we survey notations based on Euler diagrams with particular emphasis on formalization and the development of software tool support

The Semiotics of Spider Diagrams

Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first orderlogic with equality. Rather than being primarily intended for logicians,spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and itsconnection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce on which spider diagrams are based. Using Peirce's concepts and classification of signs, we analyse the ways in which different sign types are exploited in the notation. Our hope is that this analysis may be of interest beyond those readers particularly interested in spider diagrams, and act as a case study in deconstructing a simple visual logic. Along the way, we discuss the need for a deeper semiotic engagement in visual modelling

Towards a comparative evaluation of text-based specification formalisms and diagrammatic notations

Specification plays a vital role in software engineering to facilitate the development of highly dependable software. The importance of specification in software development is to serve, amongst others, as a communication tool for stakeholders in the software project. The specification also adds to the understanding of operations, and describes the properties of a system. Various techniques may be used for specification work. Z is a formal specification language that is based on a strongly-typed fragment of Zermelo-Fraenkel set theory and first-order logic to provide for precise and unambiguous specifications. Z uses mathematical notation to build abstract data, which is necessary for a specification. The role of abstraction is to describe what the system does without prescribing how it should be done. Diagrams, on the other hand, have also been used in various areas, and in software engineering they could be used to add a visual component to software specifications. It is plausible that diagrams may also be used to reason in a semi-formal way about the properties of a specification. Many diagrammatic languages are based on contours and set theory. Examples of these languages are Euler-, Spider-, Venn- and Pierce diagrams. Euler diagrams form the foundation of most diagrams that are based on closed curves. Diagrams, on the other hand, have also been used in various areas, and in software engineering they could be used to add a visual component to software specifications. It is plausible that diagrams may also be used to reason in a semi-formal way about the properties of a specification. Many diagrammatic languages are based on contours and set theory. Examples of these languages are Euler-, Spider-, Venn- and Pierce diagrams. Euler diagrams form the foundation of most diagrams that are based on closed curves. The purpose of this research is to demonstrate the extent to which diagrams can be used to represent a Z specification. A case study is used to transform the specification modelled with Z language into a diagrammatic specification. Euler, spider, Venn and Pierce diagrams are combined for this purpose, to form one diagrammatic notation that is used to transform a Z specificationSchool of ComputingM. Sc. (Information Systems

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