Theoretical Computer Science
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Retracting Some Paths in Process Algebra
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Glueing and orthogonality for models of linear logic
Theoretical Computer Science - Category theory and computer science
Geometrical semantics for linear logic (multiplicative fragment)
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
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We develop a multidimensional syntax for cut-free proofs of Multiplicative Linear Logic. This syntax is essentially equivalent to the traditional formalism of proof-nets; the interest of the multi-dimensional formalism consists in its explicit relationship with the formalism of bordisms. Bordisms are compact manifolds with boundary, which are treated as morphisms between the ‘incoming’ and ‘outgoing’ boundary components (composition is given by glueing bordisms along matching boundaries). The category of bordisms has recently become important in contemporary mathematics, in particular, because of developments in topological quantum theory and quantum gravity. A semantics of MLL underlying the multi-dimensional syntax is based on a certain category of bordisms, which we call ‘coherent space-times’. The resulting model has an extremely intuitive geometric description. The dual multiplicative connectives $\otimes$ and $\smash{\raise5.99pt\hbox{\rotatebox{-180}{\&}}}$ correspond simply to disjoint unions and connected sums of bordisms. Following ideas from topological quantum field theory, we also discover deep relationships between this new model and the author's coherent phase spaces model (Slavnov 2003), which is based on the context of symplectic geometry.