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].
This research was partly supported by EPSRC Grant EP/D038987/1.
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Abramsky, S. (2007). Full Completeness: Interactive and Geometric Characterizations of the Space of Proofs (Abstract). In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_1
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DOI: https://doi.org/10.1007/978-3-540-74915-8_1
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