Logic for specifying partially observable stochastic domains

Abstract

The authors propose a novel modal logic for specifying agent domains where the agent’s actuators and sensors are noisy, causing uncertainty in action and perception. The logic draws both on POMDP theory and logics of action and change. The development of the logic builds on previous work in which a simple multi-modal logic was augmented with first-class observation objects. These observations can then be used to represent the set of observations in a POMDP model in a natural way. In this paper, a subset of the simple modal logic is taken for the new logic, in which modal operators may not be nested. The modal operators are then extended with notions of probability. It will be shown how stochastic domains can be specified, including new kinds of axioms dealing with perception and a frame solution for the proposed logic.