An Elementary Construction for a Non-elementary Procedure
Maarten Marx, Szabolcs Mikulas
Abstract:
We consider the problem of the product finite model property for
binary products of modal logics. First we give a new proof for the
product finite model property of the logic of products of Kripke
frames, a result due to Shehtman. Then we modify the proof to obtain
the same result for logics of products of Kripke frames satisfying any
combination of seriality, reflexivity and symmetry. We do not
consider the transitivity condition in isolation because it leads to
infinity axioms when taking products.