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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| Published in: | 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 657 - 666 |
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| Main Authors: | , , |
| Format: | Conference Proceeding |
| Language: | English |
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IEEE
01.07.2015
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| ISSN: | 1043-6871 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Baaz, Matthias Reis, Giselle Leitsch, Alexander |
| Author_xml | – sequence: 1 givenname: Matthias surname: Baaz fullname: Baaz, Matthias email: baaz@logic.at – sequence: 2 givenname: Alexander surname: Leitsch fullname: Leitsch, Alexander email: leitsch@logic.at – sequence: 3 givenname: Giselle surname: Reis fullname: Reis, Giselle email: giselle.reis@inria.fr |
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| Snippet | We show an effective cut-free variant of Glivenko's theorem extended to formulas with weak quantifiers (those without eigenvariable conditions): "There is an... |
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| StartPage | 657 |
| SubjectTerms | Calculus classical logic complexity Complexity theory Computer science Context Geometry Glivenko's theorem intuitionistic logic Merging |
| Title | A Note on the Complexity of Classical and Intuitionistic Proofs |
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