  In Savage's classic decision-theoretic framework, actions are formally
defined as functions from states to outcomes. But where do the state space and
outcome space come from? Expanding on recent work by Blume, Easley, and Halpern
(BEH), we consider a language-based framework in which actions are identified
with (conditional) descriptions in a simple underlying language, while states
and outcomes (along with probabilities and utilities) are constructed as part
of a representation theorem. Our work expands the role of language from that of
BEH by using it not only for the conditions that determine which actions are
taken, but also the effects. More precisely, we take the set of actions to be
built from those of the form "do(phi)", for formulas phi in the underlying
language. This presents a problem: how do we interpret the result of do(phi)
when phi is underspecified (i.e., compatible with multiple states)? We answer
this using tools familiar from the semantics of counterfactuals: roughly
speaking, do(phi) maps each state to the "closest" phi-state. This notion of
"closest" is also something we construct as part of the representation theorem;
in effect, then, we prove that (under appropriate assumptions) the agent is
acting as if each underspecified action is first made definite and then
evaluated (i.e., by maximizing expected utility). Of course, actions in the
real world are often not presented in a fully precise manner, yet agents reason
about and form preferences among them all the same. Our work brings the
abstract tools of decision theory into closer contact with such real-world
scenarios.
