On nonmonotonic strategic reasoning Abstract   Strongxcex94Rationalizability introduces firstorder belief restrictions in the analysis of forward induction reasoning. Without actual restrictions, it coincides with Strong Rationalizability (Battigalli 2003, Battigalli and Siniscalchi 2003). These solution concepts are based on the notion of strong belief (Battigalli and Siniscalchi 2002). The nonmonotonicity of strong belief implies that the predictions of Strongxcex94Rationalizability can be inconsistent with Strong Rationalizability. I show that Strongxcex94Rationalizability refines Strong Rationalizability in terms of outcomes when the restrictions correspond to belief in a distribution over terminal nodes. Moreover, under such restrictions, the epistemic priority between rationality and belief restrictions is irrelevant for the predicted outcomes.

Regression and Progression in Stochastic Domains Abstract   Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With the exception of limited cases such as Gaussian processes over linear phenomena, belief state evolution can be complex and hard to reason with in a general way, especially when the agent has to deal with categorical assertions, incomplete information such as disjunctive knowledge, as well as probabilistic knowledge. Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive, allowing for such belief states to be expressed naturally as constraints. While that proposal is powerful, the task of how to plan effectively is not addressed. In fact, at a more fundamental level, the task of projection, that of reasoning about beliefs effectively after acting and sensing, is left entirely open.  To aid planning algorithms, we study the projection problem in this work. In the reasoning about actions literature, there are two main solutions to projection: regression and progression. Both of these have proven enormously useful for the design of logical agents, essentially paving the way for cognitive robotics. Roughly, regression reduces a query about the future to a query about the initial state. Progression, on the other hand, changes the initial state according to the effects of each action and then checks whether the formula holds in the updated state. In this work, we show how both of these generalize in the presence of degrees of belief, noisy acting and sensing. Our results allow for both discrete and continuous probability distributions to be used in the specification of beliefs and dynamics.