Labelled Deduction for the Guarded Fragment
Maarten Marx, Stefan Schlobach, Szabolcs Mikulás
Abstract:
We present the tableau calculus LC_2-TAB which is sound and complete
with respect to local square modal logic. The system is a labelled
deduction calculus in the spirit of those for modal S5. The novelty
here is that the calculus works in two interacting dimensions. This
2-dimensional modal logic allows one to simulate different other modal
logics, like K, KT, KTB or multi-K in quite an elegant way. The calculus
is also strong enough to decide an interesting pspace complete
sub-fragment of the guarded fragment, which is generally conceived of
as the true modal fragment of first order logic. A PROLOG implementation
of this calculus is available through the WWW.