Strongly Analytic Tableaux for Normal Modal Logics

A strong analytic tableau calculus is presentend for the most common normal modal logics. The method combines the advantages of both sequent-like tableaux and preexed tableaux. Proper rules are used, instead of complex closure operations for the accessibility relation, while non deter-minism and cut rules, used by sequent-like tableaux, are totally eliminated. A strong completeness theorem without cut is also given for symmetric and euclidean logics. The system gains the same modularity of Hilbert-style formulations , where the addition or deletion of rules is the way to change logic. Since each rule has to consider only adjacent possible worlds, the calculus also gains eeciency. Moreover, the rules satisfy the strong Church Rosser property and can thus be fully parallelized. Termination properties and a general algorithm are devised. The propositional modal logics thus treated +. Other logics can be constructed with diierent combinations of the proposed rules, but are not presented here.