There will be five tutorials presented at Diagrams 2021.
Title: The origin of Venn diagrams
Presenters: Jens Lemanski, Amirouche Moktefi and Lukas M. Verburgt
Venn diagrams are probably the most popular logic diagrams found in scientific liter-ature. However, they remain largely mysterious for the historian. One reason is that, unlike Euler diagrams which have many predecessors, Venn diagrams appear as if they were instantly born in the mind of a single man: John Venn (1834-1923) who published them in 1880. It is indeed unclear what process led to their invention.
Naturally, Venn is mainly remembered today for his diagrams, but a close look shows that many so-called Venn diagrams found in scientific literature are not Venn dia-grams at all. Another difficulty is that different scientific communities adopted the name for different usages. While mathematicians often refer to a certain shape having certain combinatorial properties, logicians rather refer to a tool that is specifically designed for solving a specific type of problems in logic and set theory.
The aim of this tutorial is to revisit Venn diagrams. It places them in their historical context in order to uncover their intended meaning and use. Attendees will be introduced to the origin of Venn diagrams in three parts:
The first part deals with the prehistory of Venn diagrams. Here, several pre-Venn diagrams are introduced, notably those of Schopenhauer (1820s), Krause (1830s), Mich (1870s), Kirchner (1880s) and others. These diagrams are discussed and com-pared to Venn’s scheme to identify their similarities and differences. The main aim is to uncover the type of diagrams that were used prior to the arrival of Venn on the scene and the extent to which these diagrams anticipated Venn’s scheme.
The second part covers Venn’s own invention. We trace them back to his early teach-ing at Cambridge in the 1860s and place them within the tradition of visual reasoning at Cambridge. Then, we discuss the development of Venn’s diagrams in his logic writings (1880s-90s). We particularly discuss how Venn overcame the shortcomings of earlier Eulerian diagrams and what innovations he made for the purpose. Finally, we discuss their place within his system of logic, notably in relation to his theory of existential import and his indecision about the purpose of algebraic logic itself.
The third part is devoted to the immediate reception of Venn diagrams. This gives a better grasp on their originality and how they were perceived in Venn’s time. Several logicians, including Marquand, MacColl, Macfarlane, Carroll, Peirce and Couturat commented on their merits and shortcomings. Some of the main topics include the representation of the universe, the expression of particular and disjunctive propositions, the extension of the diagrams and the construction of logic machines.
This tutorial is mainly historical and, as such, will primarily appeal to those in the Diagrams community that are interested in the history of logic diagrams. However, its topics and insights will also appeal to Diagrams community as a whole. Such topics include diagrammatic design, syntax and semantics of diagrams, inference rules and the status of diagrams in logic.
The tutorial is expected to last for some 90 minutes and is divided into three parts, each delivered by one of the organisers. A preliminary knowledge of Euler and Venn diagrams is not a pre-requisite but is encouraged. Some examples will be treated during the tutorial and hence attendees may wish to practice some of the examples before their solutions are given. Since the conference is virtual, the organisers may – in addition to their slides, and if the conference platform allows for this – make use a digital whiteboard which is open access and can be used by the participants without registration via the browser. There are no mandatory readings prior to the tutorial but the consultation of Venn’s 1880 paper “On the diagrammatic and mechanical representa-tion of propositions and reasonings” (The Philosophical Magazine) is encouraged.
Title: Extension of Venn-Peirce Diagrams: Absence of Individuals and Open Universe
Presenters: Lopamudra Choudhury, Reetu Bhattacharjee and Mihir Kumar Chakraborty
The well-known Venn-Peirce diagrams received a new dimension through the works of Shin and Hammer. After that, research in diagram studies has been activated in various directions. Chakraborty and Choudhury introduced the depiction of individuals and absence of individuals in the diagram system of Shin. Individuals were also incorporated parallelly in Spider diagrams. However, introducing absence of individuals was unique. The motivation was to be able to admit open universe and terms with no referents (empty terms). The cue was taken from traditional Indian knowledge systems.
Reetu Bhattacharjee, in her Ph.D. dissertation developed the complete systems Venni, Vennin and Vennio in which the ideas took appropriate formal shape. Her work has been published in two long papers establishing soundness and completeness of the three systems mentioned above with respect to set theoretic semantics.
The tutorial will present the three systems focusing upon Vennio (dealing with open universe). The lecture will be divided into three parts as below.
I. Motivation behind introducing absence of individuals (to be presented by Lopamudra
Choudhury).
II. The diagrams systems, their semantics, soundness and completeness results (to be presented by Reetu Bhattacharjee).
III. Empirical investigations made by Stapleton et al. through testing the effectiveness of the incorporation of absence. Concluding remarks and open questions (to be presented by Mihir K. Chakraborty).
Title: Diagrams for Belief Systems: A Tutorial in Notation and Application
Presenters: Kye Palider, Hakob Barseghyan and Paul Patton
Constructing diagrams properly calls for an interdisciplinary approach: it requires knowledge from digital humanities, human psychology, history, and philosophy. Despite the recent surge of interest in knowledge visualization, there is little agreement as to how different elements of a belief system (e.g. questions, theories, methods, reasons) can be efficiently depicted. To fill in this gap, a dia-grammatic notation with standardized conventions has been developed to allow for a unified analysis across different belief systems, and to avoid the cost, in time and effort, of learning a new diagrammatic language.
The purpose of this tutorial is to present this new diagrammatic notation and show its applicability to individual and communal belief systems across different time periods, fields of inquiry, geographies, and cultures. This notation provides intuitive techniques that help visualize the belief systems in a precise and succinct manner, without compromising the depth or quality of the depiction. The wide range of applicability, ease of use, and readily accessible resources for this diagramming notation make it a useful tool for researchers from diverse fields interested in belief systems.
The tutorial consists of a presentation and interactive workshop. In the first part of the tutorial, the participants will be introduced to the key elements of the new notation and some simple examples showing their usage. The participants will then have an opportunity to apply this notation and construct new diagrams in the second part of the tutorial. The remaining of the tutorial will be devoted to show-ing the participants some real-life examples of more complicated diagrams that have been constructed during various projects. We hope to jumpstart the partici-pants’ ability to diagram using this new notation so that they can begin to apply it in their own projects.
Title: Tutorial on Cognitive Processing of Diagrammatic Conceptual Models
Presenters: Monika Malinova and Jan Mendling
Conceptual models play an important role in the analysis and design of information
systems. Many models being used in this context are visual diagrams as for example UML Class Diagrams, Business Process Diagrams, or Use Case Diagrams, to name just a few. The bene ts of such diagrams are largely acclaimed in software engineering and information systems research; however, research on this topic is fragmented.
In this tutorial, we look at diagrams in systems analysis and design from a holistic perspective. In the rst session, we will discuss the essential characteristics of diagrams as they are frequently used in systems analysis and design. More speci cally, this session will discuss:
– Which purposes do diagrams serve in systems analysis and design?
– What are constituent properties of diagrams?
– How does problem solving with diagrams di er from text and images?
– What is the cognitive architecture required for cognitive processing of diagrams?
In the second session, we present ndings from a recent survey that we conducted
on criteria for designing e ective diagrammatic conceptual models.
– What are criteria for e ective visual processing of diagrams?
– What are criteria for e ective verbal processing of diagrams?
– What are criteria for e ective semantic processing of diagrams?
– What are criteria for e ective task processing of diagrams?
This tutorial is relevant for junior researchers and senior scholars. For junior
researchers, it is among others interesting for providing a compact overview of
various cognitive theories that could be used to understand cognitive processing
of diagrams. For senior scholars, it is interesting for its novel research insights of
a survey into 220 criteria for e ective diagram processing, organized in the four
large groups of e ective visual processing, verbal processing, semantic processing,
and task processing.
Title: Diagrams and Creativity in Civil and Architectural Engineering
Presenters: Stephanie Koerner and Lucretia Ray
In this tutorial we introduce a framework that uses diagrams to put creativity at the centre of Civil Engineering and Architecture teaching and learning undergraduate curricula in Liverpool University. We will cover interesting details of the historical precedents and current crossdisciplinary relevance of this framework – as we use it in a First Year Undergraduate module. The module grounds its summative assessment in projects that are entered into the Engineers Without Borders (EWB) UK-wide design competition programme. EWB fosters: awareness of the complex local economic, legal, social, ethical and environmental context of engineering activity” for a “globally responsible mindset”; provides students with contexts for developing skills needed address jointly locally situated and globally distributed engineering challenges; and understanding the importance for addressing such challenges of skills in communication across stakeholder diversity.
In order to help students realise these EWB purposes, we have developed and refined a
component of a first year Civil Engineering module in Liverpool University Faculty of
Engineering), entitled: “Sketching Diagrams, Maps.” Its key purpose is increase Civil and
Architectural Engineering students’ confidence in (and enjoyment of using) sketching, drawing, maps and diagrams in their assessed coursework to: observe, record, and analyse contexts; identify engineering challenges and explore and evaluate diverse possible solutions; communicate knowledge and understanding of these challenges, and present research results and projects.
Our tutorial uses examples from lectures, activities, workshops, and student presentation
sessions to show what we and the students do in “Sketching, Diagrams, Maps,” some of the key reasons why we have introduced important changes in the programme, and how we plan to improve its in future semesters. We will conclude with a series of case studies, to illustrate key points. The ideas and examples covered in this Tutorial relate to a number of the conference’s organising topics, and speak to the interests of quite a number of its attendees.