A Note on the Complexity of Classical and Intuitionistic Proofs

We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an elementary function f such that if φ is a cut-free LK proof of ⊢ A with symbol complexity ≤ c, then there exists a cut-free LJ proof...

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Vydáno v:2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science s. 657 - 666
Hlavní autoři: Baaz, Matthias, Leitsch, Alexander, Reis, Giselle
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 01.07.2015
Témata:
Calculus
classical logic
complexity
Complexity theory
Computer science
Context
Geometry
Glivenko's theorem
intuitionistic logic
Merging
ISSN:1043-6871
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Popis
Shrnutí:We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an elementary function f such that if φ is a cut-free LK proof of ⊢ A with symbol complexity ≤ c, then there exists a cut-free LJ proof of 1⊢ ⊣⊣A with symbol complexity ≤ f(c)". This follows from the more general result: "There is an elementary function f such that if φ is a cut-free LK proof of A ⊢ with symbol complexity ≤ c, then there exists a cut-free LJ proof of A ⊢ with symbol complexity ≤ f(c)". The result is proved using a suitable variant of cut-elimination by resolution (CERES) and subsumption.
ISSN:1043-6871
DOI:10.1109/LICS.2015.66