Workshop on Logical Geometry and its Applications (WoLGA 2018)

Aristotelian diagrams are compact visual representations of the elements of some logical, lexical or conceptual field, and various logical relations holding between them (e.g. contradiction and contrariety). These diagrams have a rich history in philosophical logic, which can ultimately be traced back to the works of Aristotle and Apuleius. Without a doubt, the oldest and most widely known example is the so-called ‘square of opposition’ for syllogistics, but throughout history, authors have also developed larger, more complex diagrams, such as hexagons, octagons, and even three-dimensional diagrams. In contemporary research, Aristotelian diagrams have been used in nearly all subbranches of logic, such as modal logic, various families of non-classical logics, probabilistic and fuzzy logic, consequential logic, and logics of rational agency. Furthermore, because of the ubiquity of the relations that they visualize, Aristotelian diagrams are also frequently used outside of logic, in disciplines such as philosophy, linguistics, computer science, law, cognitive science, and natural language processing. 

In recent years, Aristotelian diagrams have also begun to be studied as objects of independent logical and diagrammatic interest, giving rise to the burgeoning field of logical geometry. Rather than focusing on the specific details of any given application, logical geometry aims to develop a systematic theory of Aristotelian diagrams in general. On the logical side, it studies topics such as information level, logic-sensitivity and the interplay between Aristotelian, duality and Boolean structure; on the visual/geometrical side, it is concerned with informational vs. computational equivalence in Aristotelian diagrams, and with analyzing these diagrams as purely geometrical entities (in terms of symmetry, Euclidean distance, polyhedral duality, etc.). 

The Workshop on Logical Geometry and its Applications (WoLGA) at UNILOG 2018 aims to deepen our theoretical understanding of the logical and diagrammatic behavior of Aristotelian diagrams, as well as to broaden our perspective on their (historical and contemporary) applications.