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On the proof complexity of cut-free bounded deep inference


Reference:

Das, A., 2011. On the proof complexity of cut-free bounded deep inference. In: 20th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2011, July 4, 2011 - July 8, 2011, 2011-01-01, Bern. Heidelberg: Springer, pp. 134-148. (Lecture Notes in Computer Science)

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Abstract

It has recently been shown that cut-free deep inference systems exhibit an exponential speed-up over cut-free sequent systems, in terms of proof size. While this is good for proof complexity, there remains the problem of typically high proof search non-determinism induced by the deep inference methodology: the higher the depth of inference, the higher the non-determinism. In this work we improve on the proof search side by demonstrating that, for propositional logic, the same exponential speed-up in proof size can be obtained in bounded-depth cut-free systems. These systems retain the top-down symmetry of deep inference, but can otherwise be designed at the same depth level of sequent systems. As a result the non-determinism arising from the choice of rules at each stage of a proof is smaller than that of unbounded deep inference, while still giving access to the short proofs of deep inference.

Details

Item Type Conference or Workshop Items (UNSPECIFIED)
CreatorsDas, A.
DOI10.1007/978-3-642-22119-4_12
DepartmentsFaculty of Science > Computer Science
StatusPublished
ID Code24952

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