Chung et al., 2015; Fraccaro et al., 2017) represent states Fraccaro; or Johnson et al., 2016), but currently only implemented for R2: Encoding functions: indeed, we chose fixed but random γ . Gradient descent would be a natural choice, albeit with debatable biological plausibility. If accepted, we will include these new experimental results. Line 92: Indeed, DDC activities encode a distribution or belief about a random variable - we will amend the text. This could follow "normal" learning rules; with the DDC again ensuring that uncertainty is handled correctly.

This paper addresses the problem of biologically-plausible perceptual inference in dynamical environments. In particular, it considers situations in which informative sensory information arrives delayed with respect to the underlying state and thus require'postdiction' to update the inference of past states given new sensory observations. The authors extend a previously published method for inference in graphical models (DDC-HM) to temporally extended encoding functions and test their model in three situation cases where postdiction is relevant. Overall, I find this work valuable and interesting. It could, however, be more clearly presented and provide some relevant comparisons with alternative models.

We present an epistemic action theory for tractable epistemic reasoning as an extension to the h-approximation (HPX) theory. In contrast to existing tractable approaches, the theory supports functional fluents and postdictive reasoning with static causal laws. We argue that this combination is particularly synergistic because it allows one not only to perform direct postdiction about the conditions of actions, but also indirect postdiction about the conditions of static causal laws. We show that despite the richer expressiveness, the temporal projection problem remains tractable (polynomial), and therefore the planning problem remains in NP. We present the operational semantics of our theory as well as its formulation as Answer Set Programming.

We propose an approximation of the Possible Worlds Semantics (PWS) for action planning. A corresponding planning system is implemented by a transformation of the action specification to an Answer-Set Program. A novelty is support for postdiction wrt. (a) the plan existence problem in our framework can be solved in NP, as compared to $\Sigma_2^P$ for non-approximated PWS of Baral(2000); and (b) the planner generates optimal plans wrt. a minimal number of actions in $\Delta_2^P$. We demo the planning system with standard problems, and illustrate its integration in a larger software framework for robot control in a smart home.