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

... more >>>

Autoepistemic logic is one of the most successful formalisms for nonmonotonic reasoning. In this paper we provide a proof-theoretic analysis of sequent calculi for credulous and sceptical reasoning in propositional autoepistemic logic, introduced by Bonatti and Olivetti (ACM ToCL, 2002). We show that the calculus for credulous reasoning obeys almost ... more >>>

Recently Beyersdorff, Bonacina, and Chew (ITCS'16) introduced a natural class of Frege systems for quantified Boolean formulas (QBF) and showed strong lower bounds for restricted versions of these systems. Here we provide a comprehensive analysis of the new extended Frege system from Beyersdorff et al., denoted EF+$\forall$red, which is a ... more >>>