Tableau Calculus for Local Cubic Modal Logic and it's Implementation

In this paper we investigate the two-variable fragment of modal logics of relations interpreted on local squares, LC2. A labelled tableau calculus is presented and its soundness and completeness are proven. Further, a termination proof enables us to use the calculus as a theorem prover. The prover has been implemented in Prolog, and we give a short system description. The paper also contains examples for how the system works including translations from other modal logics into LC2.1