A Modal Logic for the Decision-Theoretic Projection Problem

We present a decidable logic in which queries can be posed about (i) the degree of belief in a propositional sentence after an arbitrary finite number of actions and observations and (ii) the utility of a finite sequence of actions after a number of actions and observations. Another contribution of this work is that a POMDP model specification is allowed to be partial or incomplete with no restriction on the lack of information specified for the model. The model may even contain information about non-initial beliefs. Essentially, entailment of arbitrary queries (expressible in the language) can be answered. A sound, complete and terminating decision procedure is provided

A Stochastic Belief Change Framework with an Observation Stream and Defaults as Expired Observations

Abstract. A framework for an agent to change its probabilistic beliefs after a stream of noisy observations is received is proposed. Observations which are no longer relevant, become default assumptions until overridden by newer, more prevalent observations. A distinction is made between background and foreground beliefs. Agent actions and environment events are distinguishable and form part of the agent model. It is left up to the agent designer to provide an environment model; a submodel of the agent model. An example of an environment model is provided in the paper, and an example scenario is based on it. Given the particular form of the agent model, several 'patterns of cognition' can be identified. An argument is made for four particular patterns