Exploring the gap between linear and classical logic

Francois Lamarche

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.


Revised 2007-12-13. Original version at
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