Resolution Is a Decision Procedure for Many Propositional Modal Logics

The paper shows satissability in many propositional modal systems, including K, KD, KT and KB, their combinations as well as their multi-modal versions, can be decided by ordinary resolution procedures. This follows from a general result that resolution and condensing is a decision procedure for the satissability problem of formulae in so-called path logics. Path logics arise from propositional and normal uni-and multi-modal logics by the optimised functional translation method. The decision result provides an alternative decision proof for the relevant modal systems, and related systems in artiicial intelligence and algebraic logic. However, this alone is not very interesting. A more far-reaching consequence of the result has practical value, namely, any standard rst-order theorem prover that is based on resolution can serve as a reasonable and eecient inference tool for modal reasoning.