The Medial rule was first devised as a deduction rule in the Calculus of Structures. In this paper we explore it from the point of view of category theory, as additional structure on a *-autonomous category. This gives us some insights on the denotational semantics of classical propositional logic, and allows us to construct new models for it, based on suitable generalizations of the theory of coherence spaces.
Keywords: *-autonomous categories, denotational semantics, linear logic, classical logic, deep inference, Medial rule
2000 MSC: 03F52, 03G30, 19D23, 18D15, 68Q55
Theory and Applications of Categories,
Vol. 18, 2007,
No. 17, pp 473-535.