Bounded situation calculus action theories

Abstract

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

Progression and Verification of Situation Calculus Agents with Bounded Beliefs

“…We show that for a very rich class of temporal properties expressed in a first-order variant of the μ-calculus verification of online executions is decidable. This result complements the one in [11], which showed decidability of verification for offline executions.…”

“…Moreover, agents often forget facts either because they are not used or because they cannot be reconfirmed. Many examples of domains modeled as bounded action theories are reported in [11], which also identifies various ways to obtain boundedness: (i) by strengthening preconditions to block actions where the bound would be exceeded; (ii) by ensuring that actions are effect bounded and never make more fluent atoms true than they make false; and (iii) by using fading fluents whose strength fades over time unless they are reconfirmed.…”

“…In Sect. 4, we go over the notion of bounded action theory from [11] and give some examples. In Sect.…”

“…In this paper, we develop a computationally-grounded framework to model and verify agents that operate in infinite domains, have incomplete information and make decisions based on their beliefs, expressed as situation calculus bounded action theories [11]. The situation calculus [33,36] is a first-order logical framework for reasoning about action, where several issues have been addressed, such as the frame problem, time, continuous change, complex actions and processes, uncertainty, and many others.…”

“…Specifically, we adopt bounded action theories [11], a particular class of action theories, for which it was shown that verification (over offline executions) of a very expressive class of first-order μ-calculus temporal properties is decidable. Bounded action theories are basic action theories [36], which entail that in all situations the number of object tuples in the extension of each fluent is bounded by a constant.…”