Improved decision procedures for Lewis's calculus S4 and von Wright's calculus M

Abstract

The decision procedures to be described in this paper constitute simplifications of methods previously developed by G. H. von Wright. The decision problems for both the systems under consideration have already been solved, but the known solutions are hopelessly impractical. Our methods for S4 and M, while not “practical” in the sense that they can be applied quickly and easily to any formula, do constitute a vast improvement over any other known methods. It appears, for example, that our methods (with the aid of very little ingenuity) will yield decisions readily when applied to modal functions of degree two (or less) with three (or fewer) distinct propositional variables.