Some prospects for semiproducts and products of modal logics

The authors study combinations (called products and semiproducts) of certain logical systems used to reason about necessity and possibility, specifically combining a logic L with the well-known S5 modal logic. They find new examples of these combinations that can be described with simple rules and still have a property called the finite model property (FMP), which helps with proving things are decidable. A key part of their work involves showing these combined systems behave in a nicely structured way when L has a limited depth, using a technique called bisimulation games. Their results help understand how certain fragments of more complex predicate modal logics can be decided. They also identify some combinations that cannot be simplified as nicely, serving as counterexamples.