Semiproducts, Products, and Modal Predicate Logics: Some Examples
Valentin Borisovich Shehtman, Dmitry Shkatov · Doklady Mathematics · 2023
We study two kinds of combined modal logics, semiproducts and products with $${\mathbf{S5}}$$ , and their connection with modal predicate logics. We present examples of propositional modal logics, for which semiproducts or products with $${\mathbf{S5}}$$ are axiomatized in the minimal way (they are called semiproduct- or product-matching with $${\mathbf{S5}}$$ ) and also present counterexamples for these properties. The finite model property for (semi)products, together with (semi)product-matching, allow us to obtain decidability of corresponding 1-variable modal predicate logics.