Independence-Friendly Modal Logic. Studies in its Expressive Power and Theoretical Relevance.

The doctoral dissertation introduces independence-friendly (IF) modal logic as an extension of standard modal logic. Making use of the notion of uniform strategy, a game-theoretical interpretation of IF modal logic is formulated. It is shown that under this interpretation, IF modal logic has greater expressive power than standard modal logic, and can be translated into first-order logic. However, when restricted to a simple tense-logical setting (evaluation over strict linear orders), its expressive power coincides with standard tense logic. The syntax of IF modal logic can be modified to allow independence of modal operators from conjunctions and disjunctions. It is shown that the resulting modal logic can no longer be translated into first-order logic. Two further interpretations of the language of IF modal logic are given, one in terms of backwards-looking operators, the other algebraic. The dissertation contains an extensive discussion of tenses in linguis- tics, and explains how the 'backwards-looking operators' interpretation of IF tense logic makes it possible to formally distinguish between two types of independence appearing in connection with tense evaluation. It is argued that the linguistic critique against scope theories of tense becomes less appealing when this distinction is made.