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.