Event Domains, Stable Functions and Proof-Nets

  • Authors:
  • Samson Abramsky

  • Affiliations:
  • Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford OX1 3QD, U.K.

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2007

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Abstract

We pursue the program of exposing the intrinsic mathematical structure of the ''space of proofs'' of a logical system [S. Abramsky and R. Jagadeesan. Games and Full Completeness for Multiplicative Linear Logic, Journal of Symbolic Logic, (1994), vol. 59, no. 2, 543-574]. 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. This work forms part of a continuation of previous joint work with Radha Jagadeesan [S. Abramsky and R. Jagadeesan. Games and Full Completeness for Multiplicative Linear Logic, Journal of Symbolic Logic, (1994), vol. 59, no. 2, 543-574] and Paul-Andre Mellies [S. Abramsky and P.-A. Mellies. Concurrent Games and Full Completeness. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, 431-44, 1999].