Abstract
This paper presents a linear time algorithm for proof verification on N-Graphs. This system, introduced by de Oliveira, incorporates the geometrical techniques from the theory of proof-nets to present a multiple-conclusion calculus for classical propositional logic. The soundness criterion is based on the one given by Danos and Regnier for Linear Logic. We use a DFS-like search to check the validity of the cycles in a proof graph, and some properties from trees to check the connectivity of every switching (a concept similar to D-R graph). Since the soundness criterion in proof graphs is analogous to Danos-Regnier’s procedure, the algorithm can also be extended to check proofs in the multiplicative linear logic without units (MLL−) with linear time complexity.
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References
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Andrade, L., Carvalho, R., de Oliveira, A., de Queiroz, R. (2013). Linear Time Proof Verification on N-Graphs: A Graph Theoretic Approach. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2013. Lecture Notes in Computer Science, vol 8071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39992-3_7
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DOI: https://doi.org/10.1007/978-3-642-39992-3_7
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