On the Verification of Belief Programs
This work addresses verification challenges for belief programs, which are incremental in extending prior frameworks for high-level robot control under uncertainty.
The paper tackles the problem of verifying belief programs, a probabilistic extension of GOLOG programs for robot control under uncertainty, by proposing a formalism based on modal logic to specify properties and investigating the decidability and undecidability of verification.
In a recent paper, Belle and Levesque proposed a framework for a type of program called belief programs, a probabilistic extension of GOLOG programs where every action and sensing result could be noisy and every test condition refers to the agent's subjective beliefs. Inherited from GOLOG programs, the action-centered feature makes belief programs fairly suitable for high-level robot control under uncertainty. An important step before deploying such a program is to verify whether it satisfies properties as desired. At least two problems exist in doing verification: how to formally specify properties of a program and what is the complexity of verification. In this paper, we propose a formalism for belief programs based on a modal logic of actions and beliefs. Among other things, this allows us to express PCTL-like temporal properties smoothly. Besides, we investigate the decidability and undecidability for the verification problem of belief programs.