Proofnets and Context Semantics for the Additives
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We provide a context semantics for Multiplicative-Additive Linear Logic (MALL), together with proofnets whose reduction preserves semantics, where proofnet reduction is equated with cut-elimination on MALL sequents. The results extend the program of Gonthier, Abadi, and Lévy, who provided a “geometry of optimal λ-reduction” (context semantics) for λ-calculus and Multiplicative-Exponential Linear Logic (MELL). We integrate three features: a semantics that uses buses to implement slicing; a proofnet technology that allows multidimensional boxes and generalized garbage, preserving the linearity of additive reduction; and finally, a read-back procedure that computes a cut-free proof from the semantics, a constructive companion to full abstraction theorems.
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- Proofnets and Context Semantics for the Additives
- Book Title
- Computer Science Logic
- Book Subtitle
- 16th International Workshop, CSL 2002 11th Annual Conference of the EACSL Edinburgh, Scotland, UK, September 22–25, 2002 Proceedings
- pp 151-166
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- Online ISBN
- Series Title
- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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- Springer-Verlag Berlin Heidelberg
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- Julian Bradfield (4)
- Editor Affiliations
- 4. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh
- Author Affiliations
- 5. Computer Science Department, Brandeis University Waltham, Massachusetts, 02454
- 6. École Normale Superieure, 45 rue d’Ulm, 75005, Paris
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