Non-primitive recursive decidability of products of modal logics with expanding domains

We show that--unlike products of `transitive' modal logics which are usually undecidable-their `expanding domain' relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component--call it the `flow of time'--is

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: David Gabelaia, Agi Kurucz, Frank Wolter, Michael Zakharyaschev
• Keywords: APAL 2006, Dynamic Topological Logic, Logic, Recursive Time