  Standard models of multi-agent modal logic do not capture the fact that
information is often ambiguous, and may be interpreted in different ways by
different agents. We propose a framework that can model this, and consider
different semantics that capture different assumptions about the agents'
beliefs regarding whether or not there is ambiguity. We consider the impact of
ambiguity on a seminal result in economics: Aumann's result saying that agents
with a common prior cannot agree to disagree. This result is known not to hold
if agents do not have a common prior; we show that it also does not hold in the
presence of ambiguity. We then consider the tradeoff between assuming a common
interpretation (i.e., no ambiguity) and a common prior (i.e., shared initial
beliefs).
