A draft of my “Two Puzzles about Ability Can” is now available in the Research section.
Here is the abstract:

The received wisdom on ability modals is that they differ from their epistemic and deontic cousins in what inferences they license and better receive a universal or conditional analysis instead of an existential one. The goal of this paper is to sharpen the empirical picture about the semantics of ability modals, and to propose an analysis that explains what makes the can of ability so special but that also preserves the crucial intuition that all uses of can share a common lexical semantics. The resulting framework combines tools and techniques from dynamic and inquisitive semantics with insights from the literature of the the role of agency in deontic logic. It explains not only why the canof ability, while essentially being an existential modal operator, sometimes resists distribution over disjunction and interacts with its duals in particular and hitherto unnoticed ways, but also has a tendency to license free choice inferences.