No Feasible Monotone Interpolation for Cut-free Gentzen Type Propositional Calculus with Permutation Inference
نویسنده
چکیده
The feasible monotone interpolation method has been one of the main tools to prove the exponential lowerbounds for relatively weak propositional systems. In [2], we introduced a simple combinatorial reasoning system, GCNF+permutation, as a candidate for an automatizable, though powerful, propositional calculus. We show that the monotone interpolation method is not applicable to prove the superpolynomial lower bounds for GCNF+permutation. At the same time, we show that Cutting Planes, Hilbert's Nullstellensatz and the polynomial calculus do not p-simulate GCNF+permutation. keywords: automated theorem proving, proof complexity, Craig's interpolation theorem, proof theory
منابع مشابه
Tractability of Cut-Free Gentzen Type Propositional Calculus with Permutation Inference
In Arai (1996), we introduced a new inference rule called permutation to propositional calculus and showed that cut-free Gentzen system LK (GCNF) with permutation (1) satis es the feasible subformula property, and (2) proves pigeonhole principle and k-equipartition polynomially. In this paper, we survey more properties of our system. First, we prove that cut-free LK + permutation has polynomial...
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