Theoretical Computer Science
Proofs and types
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
New foundations for the geometry of interaction
Information and Computation
Proof-nets and the Hilbert space
Proceedings of the workshop on Advances in linear logic
Geometry of interaction III: accommodating the additives
Proceedings of the workshop on Advances in linear logic
Geometry of interaction 2: deadlock-free algorithms
COLOG '88 Proceedings of the International Conference on Computer 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
Geometry of Interaction and linear combinatory algebras
Mathematical Structures in Computer Science
Unique decomposition categories, Geometry of Interaction and combinatory logic
Mathematical Structures in Computer Science
On the Geometry of Interaction for Classical Logic
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
A categorical model for the geometry of interaction
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
From Geometry of Interaction to Denotational Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Towards a typed geometry of interaction
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Towards a typed geometry of interaction
Mathematical Structures in Computer Science
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Girard's Geometry of Interaction (GoI) develops a mathematical framework for modelling the dynamics of cut-elimination. In previous work we introduced a typed version of GoI, called Multiobject GoI (MGoI) for multiplicative linear logic [Haghverdi, E. and Scott, P.J. (2005), Towards a Typed Geometry of Interaction, CSL2005 (Computer Science Logic), Luke Ong, Ed. SLNCS 3634, 216-231]. This was later extended to cover the exponentials by the first author [Haghverdi, E. (2006), Typed GoI for Exponentials. in: M. Bugliesi et al. (Eds.): Proc. of ICALP 2006, Part II, LNCS 4052, 384-395. Springer Verlag]. Our development of MGoI depends on a new theory of partial traces, as well as an abstract notion of orthogonality (related to work of Hyland and Schalk.) In this paper we recall the MGoI semantics for MLL, and discuss how it relates to denotational semantics of MLL in certain *-autonomous categories. Finally, we prove characterization theorems for the MGoI interpretation of MLL in partially traced categories with an orthogonality, and for the original untyped GoI interpretation of MLL in a traced unique decomposition category.