🤖 AI Summary
This study investigates the axiomatizability, finite model property, and decidability of products and semi-products of modal logics L and S5 under locally bounded depth. By integrating bisimulation games with algebraic semantics and model-theoretic techniques, the authors establish minimal axiomatizations for several product and semi-product logics and prove that these logics enjoy the product (semi-product) finite model property. They also construct explicit counterexamples demonstrating that certain such logics are not minimally axiomatizable. Furthermore, the paper establishes the local tabularity of these logics, from which it derives the decidability of first-order modal logic QL and its one-variable fragment extended with the Barcan formula.
📝 Abstract
We consider products and semiproducts of propositional modal logics L with S5 and present new examples of product and semiproduct logics axiomatized in the minimal way and enjoying the product (or semiproduct) FMP. An essential part of the proof is local tabularity of these (semi)products for L of finite depth; it is obtained by using bisimulation games. These results readily imply decidability for 1-variable fragments of predicate modal logics QL and QL+Barcan formula. We also present new counterexamples, i.e. (semi)products not axiomatizable in the simplest way.