#
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.

http://www.tac.mta.ca/tac/volumes/18/17/18-17.dvi

http://www.tac.mta.ca/tac/volumes/18/17/18-17.ps

http://www.tac.mta.ca/tac/volumes/18/17/18-17.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/17/18-17.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/17/18-17.ps

Revised 2007-12-13. Original version at

http://www.tac.mta.ca/tac/volumes/18/17/18-17a.dvi

TAC Home