Diagrammatic Logics
Facilitators: Dr Gem Stapleton and Dr Jim Burton
Course Summary
This is an introductory course on diagrammatic logics. It will cover the historical development of diagrammatic logics and introduce delegates to the existing state-of-the-art results in this field. The emphasis will be on the formalization of such logics and how to reason formally with them. Key formal properties such as soundness, completeness, decidability and expressiveness will be covered. The course will be very interactive, including ample time for attendees to attempt exercises to reinforce theoretical ideas covered during the lectures. The exercises will be designed also to allow attendees to explore the boundaries of knowledge and to start thinking about original directions that their own research may follow, after the Winter School.
Prerequisite Knowledge
Attendees should have working knowledge of set theory and logic, including logical inference. No previous knowledge on diagrammatic logics is necessary. Delegates should be interested in diagrammatic logics from a mathematical perspective.
Course Outcomes
On completing the course, attendees should have a broad knowledge of the existing state-of-the-art in research into diagrammatic logics. They should be well placed to extend their knowledge in areas of particular interest and able to identify key contributions in the literature. Further, they should be able to start identifying gaps in knowledge and begin to be able to scope a research project in this area.
Course Materials
Session 1: Introduction to Diagrammatic Logics
Session 2: Syntax and Semantics of Euler Diagrams
Session 3: Inference
Session 4: Formal Properties of Diagrammatic Logics
Material for all sessions in one file as presented and in handout form.
Other Resources
Research paper of core importance to the course.
Central text on spider diagrams.
Paper looking at choices of inference rules for Euler diagrams.
Many of Dr Stapleton's publications can be downloaded from her web site.