Cross-World Predication in Belief Reports

Abstract

Some sentences of natural language, construed in terms of possible world semantics, describe cross-world relations. Among them are some belief reports like I thought your yacht was larger than it is, and prescriptions about beliefs like You should not underestimate people. Standard modal semantics cannot capture the truth conditions of such sentences because, in standard semantics, predicates can only have intra-world extensions. In order to be able to analyze sentences of this sort, we need a semantics providing a cross-world interpretation of predicates and capable of evaluating sentences at sequences of possible worlds rather than single possible worlds. Butterfield and Stirling offered a system of temporal logic of this sort. More recently, Wehmeier offered an alethic logic of this sort. However, the applicability of their systems to relevant types of discourse is substantially restricted. In the paper, a semantic system is developed that is applicable to doxastic and deontic-doxastic contexts without restriction.