Fibring Semantic Tableaux

The methodology of fibring is a successful framework for combining logical systems based on combining their semantics. In this paper, we extend the fibring approach to calculi for logical systems: we describe how to uniformly construct a sound and complete tableau calculus for the combined logic from calculi for the component logics. We consider semantic tableau calculi that satisfy certain conditions and are therefore known to be “well-behaved”—such that fibring is possible. The identification and formulation of conditions that are neither too weak nor too strong is a main contribution of this paper. As an example, we fibre tableau calculi for first order predicate logic and for the modal logic K.