  Under what circumstances can a system be said to have beliefs and goals, and
how do such agency-related features relate to its physical state? Recent work
has proposed a notion of interpretation map, a function that maps the state of
a system to a probability distribution representing its beliefs about an
external world. Such a map is not completely arbitrary, as the beliefs it
attributes to the system must evolve over time in a manner that is consistent
with Bayes' theorem, and consequently the dynamics of a system constrain its
possible interpretations. Here we build on this approach, proposing a notion of
interpretation not just in terms of beliefs but in terms of goals and actions.
To do this we make use of the existing theory of partially observable Markov
processes (POMDPs): we say that a system can be interpreted as a solution to a
POMDP if it not only admits an interpretation map describing its beliefs about
the hidden state of a POMDP but also takes actions that are optimal according
to its belief state. An agent is then a system together with an interpretation
of this system as a POMDP solution. Although POMDPs are not the only possible
formulation of what it means to have a goal, this nevertheless represents a
step towards a more general formal definition of what it means for a system to
be an agent.
