A Simple Tableau System for the Logic of Elsewhere

We analyze different features related to the mechanization of von Wright’s logic of elsewhere E . First, we give a new proof of the NP-completeness of the satisfiability problem (giving a new bound for the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense to be specified). Second, we present a prefixed tableau system for E and we prove both its soundness and completeness. Two extensions of this system are also defined, one related to the logical consequence relation and the other related to the addition of modal operators (without increasing the expressive power). An example of tableau proof is also presented. Different continuations of this work are proposed, one of them being to implement the defined tableau system, another one being to extend this system to richer logics that can be found in the literature.