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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 [2006], 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 Blume, Easley, and Halpern 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. 

We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models. PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to incorporate new information and restructure the representation. We show by example how PDGs are an especially natural modeling tool. We provide three semantics for PDGs, each of which can be derived from a scoring function (on joint distributions over the variables in the network) that can be viewed as representing a distribution's incompatibility with the PDG. For the PDG corresponding to a BN, this function is uniquely minimized by the distribution the BN represents, showing that PDG semantics extend BN semantics. We show further that factor graphs and their exponential families can also be faithfully represented as PDGs, while there are significant barriers to modeling a PDG with a factor graph. 

We investigate how to model the beliefs of an agent who becomes more aware. We use the framework of Halpern and R\^ego [2013], expanded by adding probability, and define a notion of a model transition that describes constraints on how, if an agent becomes aware of a new formula phi in state s of a model M, she transitions to state s* in a model M*. We then discuss how such a model can be applied to information disclosure.