Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4663176 | Journal of Applied Logic | 2006 | 12 Pages |
We generalise the result of [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34] on decidability of the two variable monadic guarded fragment of first order logic with constraints on the guard relations expressible in monadic second order logic. In [H. Ganzinger, C. Meyer, M. Veanes, The two-variable guarded fragment with transitive relations, in: Proc. 14th IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, 1999, pp. 24–34], such constraints apply to one relation at a time. We modify their proof to obtain decidability for constraints involving several relations. Now we can use this result to prove decidability of multi-modal modal logics where conditions on accessibility relations involve more than one relation. Our main application is intuitionistic modal logic, where the intuitionistic and modal accessibility relations usually interact in a non-trivial way.