Abstraction of Nondeterministic Situation Calculus Action Theories -- Extended Version

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.

Bounded Situation Calculus Action Theories

In this paper, we investigate bounded action theories in the situation calculus. A bounded action theory is one which entails that, in every situation, the number of object tuples in the extension of fluents is bounded by a given constant, although such extensions are in general different across the infinitely many situations. We argue that such theories are common in applications, either because facts do not persist indefinitely or because the agent eventually forgets some facts, as new ones are learnt. We discuss various classes of bounded action theories. Then we show that verification of a powerful first-order variant of the mu-calculus is decidable for such theories. Notably, this variant supports a controlled form of quantification across situations. We also show that through verification, we can actually check whether an arbitrary action theory maintains boundedness.