The Advent of Formal Diagrammatic Reasoning Systems

In knowledge representation and reasoning systems, diagrams have many practical applications and are used in numerous settings. Indeed, it is widely accepted that diagrams are a valuable aid to intuition and help to convey ideas and information in a clear way. On the other side, logicians have viewed diagrams as informal tools, but which cannot be used in the manner of formal argumentation. Instead, logicians focused on symbolic representations of logics. Recently, this perception was overturned in the mid 1990s, first with seminal work by Shin on an extended version of Venn diagrams. Since then, certainly a growth in the research field of formal reasoning with diagrams can be witnessed. This paper discusses the evolution of formal diagrammatic logics, focusing on those systems which are based on Euler and Venn-Peirce diagrams, and Peirces existential graphs. Also discussed are some challenges faced in the area, some of which are specifically related to diagrams.