On Friday, June 27th, Dr John Stell from the University of Leeds, UK, will give a talk at JAIST.
Bi-Intuitionistic Modal Logic and Hypergraphs
I will discuss motivations from spatial reasoning and mathematical morphology (as used in image processing) for the notion of a relation on a graph. I will show how the algebra of these relations is weaker than that of relations on a set. This leads to a generalization of relation algebras in which the Boolean algebra is replaced by a symmetric Heyting algebra.
These relations can be used as the accessibility relations for a modal logic in which propositions are interpreted as subgraphs of a graph or more generally a hypergraph.