Fusions of Modal Logics Revisited

The fusion L l\Omega L r of two normal modal logics formulated in languages with disjoint sets of modal operators is the smallest normal modal logic containing L l [ L r . This paper proves that decidability, interpolation, uniform interpolation, and Halld'encompleteness are preserved under forming fusions of normal polyadic polymodal logics. Those problems remained open in [Fine & Schurz [3]] and [Kracht & Wolter [10]]. The paper defines the fusion ` l\Omega ` r of two classical modal consequence relations and proves that decidability transfers also in this case. Finally, these results are used to prove a general decidability result for modal logics based on superintuitionistic logics. Given two logical system L 1 and L 2 it is natural to ask whether the fusion (or join) L 1\Omega L 2 of them inherits the common properties of both L 1 and L 2 . Let us consider some examples: (i) It is known that the first order theory of one equivalence relation has the finite model property an..