Value Types in Eiffel

Identifies a number of problems with Eiffel's expanded types in modelling value types, and proposes a backward compatible syntactic extension, and a modified semantics. The latter is also shown to be (effectively) backward compatible, in the sense that existing programs would run unaffected if compilers implemented the new semantics. The benefits of the approach are discussed, including an elegant approach to rebuilding data structure libraries

Reasoning with Spider Diagrams

Spider diagrams combine and extend Venn diagrams and Euler circles to express constraints on sets and their relationships with other sets. These diagrams can usefully be used in conjunction with object-oriented modelling notations such as the Unified Modelling Language. This paper summarises the main syntax and semantics of spider diagrams and introduces four inference rules for reasoning with spider diagrams and a rule governing the equivalence of Venn and Euler forms of spider diagrams. This paper also details rules for combining two spider diagrams to produce a single diagram which retains as much of their combined semantic information as possible and discusses disjunctive diagrams as one possible way of enriching the system in order to combine spider diagrams so that no semantic information is lost

A New Language for the Visualization of Logic and reasoning

Many visual languages based on Euler diagrams have emerged for expressing relationships between sets. The expressive power of these languages varies, but the majority can only express statements involving unary relations and, sometimes, equality. We present a new visual language called Visual First Order Logic (VFOL) that was developed from work on constraint diagrams which are designed for software specification. VFOL is likely to be useful for software specification, because it is similar to constraint diagrams, and may also fit into a Z-like framework. We show that for every First Order Predicate Logic (FOPL) formula there exists a semantically equivalent VFOL diagram. The translation we give from FOPL to VFOL is natural and, as such, VFOL could also be used to teach FOPL, for example

Some Results for Drawing Area Proportional Venn3 With Convex Curves

Many data sets are visualized effectively with area proportional Venn diagrams, where the area of the regions is in proportion to a defined specification. In particular, Venn diagrams with three intersecting curves are considered useful for visualizing data in many applications, including bioscience, ecology and medicine. To ease the understanding of such diagrams, using restricted nice shapes for the curves is considered beneficial. Many research questions on the use of such diagrams are still open. For instance, a general solution to the question of when given area specifications can be represented by Venn3 using convex curves is still unknown. In this paper we study symmetric Venn3 drawn with convex curves and show that there is a symmetric area specification that cannot be represented with such a diagram. In addition, by using symmetric diagrams drawn with polygons, we show that, if area specifications are restricted so that the double intersection areas are no greater than the triple intersection area then the specification can be drawn with convex curves. We also propose a construction that allows the representation of some area specifications when the double intersection areas are greater than the triple intersection area. Finally, we present some open questions on the topic

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

Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets

Area-proportional Euler diagrams representing three sets are commonly used to visualize the results of medical experiments, business data, and information from other applications where statistical results are best shown using interlinking curves. Currently, there is no tool that will reliably visualize exact area-proportional diagrams for up to three sets. Limited success, in terms of diagram accuracy, has been achieved for a small number of cases, such as Venn-2 and Venn-3 where all intersections between the sets must be represented. Euler diagrams do not have to include all intersections and so permit the visualization of cases where some intersections have a zero value. This paper describes a general, implemented, method for visualizing all 40 Euler-3 diagrams in an area-proportional manner. We provide techniques for generating the curves with circles and convex polygons, analyze the drawability of data with these shapes, and give a mechanism for deciding whether such data can be drawn with circles. For the cases where non-convex curves are necessary, our method draws an appropriate diagram using non-convex polygons. Thus, we are now always able to automatically visualize data for up to three sets

How Should We Use Colour in Euler Diagrams?

This paper addresses the problem of how best to use colour in Euler diagrams. The choice of using coloured curves, rather than black curves, possibly with coloured fill is often made in tools that automatically draw Euler diagrams for information visualization as well as when they are drawn manually. We address the problem by empirically evaluating various different colour treatments: coloured or black curves combined with either no fill or coloured fill. By collecting performance data, we conclude that Euler diagrams with coloured curves and no fill significantly outperform all other colour treatments. Most automated layout algorithms adopt colour fill and are, thus, reducing the effectiveness of the Euler diagrams produced. As Euler diagrams can be used in a multitude of areas, ranging from crime control to social network analysis, our results stand to increase the ability of users to accurately and quickly extract information from their visualizations

The Empirical Development of a Preparation for Marriage Curriculum for Twelfth-Grade Students

Problem. The purpose of this project was to develop an instructional product that would enrich the student\u27s knowledge about dating and marriage, and teach specific relational skills. Method. A systematic procedure was undertaken in the development and validation of the product. First, the content of a pre-marriage course was identified through an examination of a large sample of family-life texts, a survey of teacher criticisms and recommendations pertaining to the text Marriage (Christensen, 1980), and an analysis of a group of 317 youth using the Search Institute instrument, Youth Research Survey (Strommen, 1977; see appendix E). Second, the proposed content subjects were divided into instructional units, arranged in a logical sequence, and introduced with behavioral objectives. Third, literature and research in the various unit content areas was reviewed and a prototype of the pre-marriage curriculum drafted. This prototype curriculum was taught to thirty-two seniors in a parochial academy in Hagerstown, Maryland. Validation of the instructional units was considered successful when 80 percent of the students achieved 80 percent mastery in each objective. Twenty four percent of the objectives failed to reach this level. Fourth, each of the instructional units were expanded, weaknesses exposed during the tryout stage were corrected, and a teacher\u27s manual was prepared. Finally, the instructional product was taught to class of seventeen twelfth-grade students at a parochial academy, Battle Creek, Michigan. Results. The instructional product met the validation criterion-- 80 percent of the students fulfilled each objective at or above the 80 percent mastery level. Conclusions. It was concluded that the instructional product was successful and, with some modification, ready for further use as an enrichment resource for pre-marriage courses. It was recommended that further systematic revision of the product take place based on student performance

Does the Orientation of an Euler Diagram Affect User Comprehension?

Euler diagrams, which form the basis of numerous visual languages, can be an effective representation of information when they are both well-matched and well-formed. However, being well-matched and well-formed alone does not imply effectiveness. Other diagrammatical properties need to be considered. Information visualization theorists have known for some time that orientation has the potential to affect our interpretation of diagrams. This paper begins by explaining why well-matched and well-formed drawing principles are insufficient and discusses why we should study the orientation of Euler diagrams. To this end an empirical study is presented, designed to observe the effect of orientation upon the comprehension of Euler diagrams. The paper concludes that the orientation of Euler diagrams does not significantly affect comprehension

Semantics Through Pictures: towards a diagrammatic semantics for object-oriented modelling notations

An object-oriented (OO) model has a static component, the set of allowable snapshots or system states, and a dynamic component, the set of filmstrips or sequences of snapshots. Diagrammatic notations, such as those in UML, each places constraints on the static and/or dynamic models. A formal semantics of OO modeling notations can be constructed by providing a formal description of (i) sets of snapshots and filmstrips, (ii) constraints on those sets, and (iii) the derivation of those constraints from diagrammatic notations. In addition, since constraints are contributed by many diagrams for the same model, a way of doing this compositionally is desirable. One approach to the semantics is to use first-order logic for (i) and (ii), and theory inclusion with renaming, as in Larch, to characterize composition. A common approach to (iii) is to bootstrap: provide a semantics for a kernel of the notation and then use the kernel to give a semantics to the other notations. This only works if a kernel which is sufficiently expressive can be identified, and this is not the case for UML. However, we have developed a diagrammatic notation, dubbed constraint diagrams, which seems capable of expressing most if not all static and dynamic constraints, and it is proposed that this be used to give a diagrammatic semantics to OO models