Handbook_of_Modal_Logic

The first perspective emphasises the descriptive range of modal logic as the study of key concepts and the reasoning patterns they give rise to. The second perspective emphasises the methodological aspect of fine-structure: modal languages bring to light the inner structure of classical systems. But these views are not in conflict. As the Handbook makes abundantly clear, most active research directions in modal logic take something from both. Indeed, the most widespread semantics of modal logic in terms of relational models (used in virtually every chapter of the Handbook) provides a setting in which these perspectives coexist fruitfully. Moreover, the two views help us better understand historical contributions made in the field. For example, the modal system S4 was introduced in the 1920s as an analysis of the concept of necessary implication. But the limited expressive power of the formalism as an account of implicative structure turned out to be the key to S4’s wide range of other applications, and its attractive mathematical behaviour. In short, both perspectives on modal logic are widely applicable, and both have proved historically robust. Let’s take a closer look at them, and see how they are related