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.
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Marx, M., Mikulás, S., Schlobach, S. (2000). Labelled Deduction for the Guarded Fragment. In: Basin, D., D’Agostino, M., Gabbay, D.M., Matthews, S., Viganò, L. (eds) Labelled Deduction. Applied Logic Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4040-9_8
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DOI: https://doi.org/10.1007/978-94-011-4040-9_8
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