Local is Best: Efficient Reductions to Modal Logic K

Abstract

We present novel reductions of extensions of the basic modal logic {textsf {K} } with axioms textsf {B} , textsf {D} , textsf {T} , textsf {4} and textsf {5} to Separated Normal Form with Sets of Modal Levels textsf {SNF} _{sml}. The reductions typically result in smaller formulae than the reductions by Kracht. The reductions to textsf {SNF} _{sml} combined with a reduction to textsf {SNF} _{ml} allow us to use the local reasoning of the prover {text {K}_{text {S}}}{text {P}} to determine the satisfiability of modal formulae in the considered logics. We show experimentally that the combination of our reductions with the prover {text {K}_{text {S}}}{text {P}} performs well when compared with a specialised resolution calculus for these logics, the built-in reductions of the first-order prover SPASS, and the higher-order logic prover LEO-III.