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]. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Abramsky, S. (2007). Full completeness: Interactive and geometric characterizations of the space of proofs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4646 LNCS, pp. 1–2). Springer Verlag. https://doi.org/10.1007/978-3-540-74915-8_1
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