Event Domains, Stable Functions and Proof-Nets

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-André Melliès [S. Abramsky and P.-A. Melliès. Concurrent Games and Full Completeness. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, 431–44, 1999].