Abstraction of Nondeterministic Situation Calculus Action Theories -- Extended Version
This work addresses strategic reasoning and synthesis for agents in nondeterministic environments, but it appears incremental as it extends existing theories with a new abstraction setting.
The paper tackles the problem of abstracting agent behavior in nondeterministic domains by developing a framework based on the nondeterministic situation calculus and ConGolog, showing that if an agent has a strong FOND plan at an abstract level, there exists a refinement that achieves the goal at the concrete level.
We develop a general framework for abstracting the behavior of an agent that operates in a nondeterministic domain, i.e., where the agent does not control the outcome of the nondeterministic actions, based on the nondeterministic situation calculus and the ConGolog programming language. We assume that we have both an abstract and a concrete nondeterministic basic action theory, and a refinement mapping which specifies how abstract actions, decomposed into agent actions and environment reactions, are implemented by concrete ConGolog programs. This new setting supports strategic reasoning and strategy synthesis, by allowing us to quantify separately on agent actions and environment reactions. We show that if the agent has a (strong FOND) plan/strategy to achieve a goal/complete a task at the abstract level, and it can always execute the nondeterministic abstract actions to completion at the concrete level, then there exists a refinement of it that is a (strong FOND) plan/strategy to achieve the refinement of the goal/task at the concrete level.