Uniform Definability in Assertability Semantics

This paper compares two notions of expressive power for a logical language and shows how they come apart. In particular, it introduces a simple framework called assertability semantics for handling puzzling features of the interaction of epistemic modals and disjunction. As a consequence of the solution to those puzzles, it is shown that the disjunction is in fact definable: every sentence is equivalent to a sentence without disjunction. But we then prove that the disjunction is not uniformly definable: no schematic definition of it can be given in terms of the other connectives of the fragment. We also consider the extension with inquisitive disjunction and prove that it is expressively complete.