Albert Atserias, Nicola Galesi, Ricard GavaldÃ

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 ...
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Albert Atserias, Nicola Galesi, Pavel Pudlak

We show that an LK proof of size $m$ of a monotone sequent (a sequent

that contains only formulas in the basis $\wedge,\vee$) can be turned

into a proof containing only monotone formulas of size $m^{O(\log m)}$

and with the number of proof lines polynomial in $m$. Also we show

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