Monotone simulations of non-monotone proofs
نویسندگان
چکیده
منابع مشابه
Monotone Simulations of Nonmonotone Proofs
We show that an LK proof of size m of a monotone sequent (a sequent that contains only formulas in the basis ∧,∨) can be turned into a proof containing only monotone formulas of size mO(log m) and with the number of proof lines polynomial in m. Also we show that some interesting special cases, namely the functional and the onto versions of PHP and a version of the Matching Principle, have polyn...
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We show that an LK proof of size m of a monotone sequent (a sequent that contains only formulas in the basis ∧,∨) can be turned into a proof containing only monotone formulas of size mO(log m) and with the number of proof lines polynomial in m. Also we show that some interesting special cases, namely the functional and the onto versions of PHP and a version of the Matching Principle, have polyn...
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Atserias, Galesi, and Pudlák [4] have shown that the monotone sequent calculus MLK quasipolynomially simulates proofs of monotone sequents in the full sequent calculus LK (or equivalently, in Frege systems). We generalize the simulation to the fragment MCLK of LK which can prove arbitrary sequents, but restricts cut-formulas to be monotone. We also show that MLK as a refutation system for CNFs ...
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We study the complexity of proving the Pigeon Hole Principle (PHP) in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We show that the standard encoding of the PHP as a monotone sequent admits quasipolynomial-size proofs in this system. This result is a consequence of deriving the basic properties of certain quasipolynomial-size monotone formulas computing the boolean...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2002
ISSN: 0022-0000
DOI: 10.1016/s0022-0000(02)00020-x