Full completeness: interactive and geometric characterizations of the space of proofs

Authors:
Samson Abramsky
Affiliations:
Oxford University Computing Laboratory, Oxford, UK
Venue:
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Year:
2007

Citing 5
Cited 0

Linear logic

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LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Event Domains, Stable Functions and Proof-Nets

Electronic Notes in Theoretical Computer Science (ENTCS)

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Abstract

We pursue the program of exposing the intrinsic mathematical structure of the "space of a proofs" of a logical system [AJ94b]. We study the case of Multiplicative-Additive Linear Logic (MALL). We use tools from Domain theory to develop a semantic notion of proof net for MALL, and prove a Sequentialization Theorem. We also give an interactive criterion for strategies, formalized in the same Domain-theoretic setting, to come from proofs, and show that a "semantic proof structure" satisfies the geometric correctness criterion for proof-nets if and only if it satisfies the interactive criterion for strategies. We also use the Domain-theoretic setting to give an elegant compositional account of Cut-Elimination. This work is a continuation of previous joint work with Radha Jagadeesan [AJ94b] and Paul-André Melliès [AM99].