Handbook of Automated Reasoning

4.3 Expressive power

Now that we have introduced the standard relational translation, which identifies modal languages as fragments of first-order or other predicate logics, let us take a closer look at what we have actually obtained. We will first consider matters related to expressive power, and then, in Section 4.4, focus on computing with translations of nonclassical formulae. In particular, we will first look at semantic characterizations of the modal fragment in terms of bisimulations; after that we consider several explanations for the good logical and computational behavior of the modal fragment.

By Theorem 4.2, a modal formula A of the basic modal language can be viewed as a unary FO formula α(x). How much of FO does this modal fragment ...