Abstract
We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories.
Highlights
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]
As a result a basic action theory D is the union of the following disjoint sets: the foundational, domain independent, axioms of the situation calculus (Σ); action precondition axioms stating when actions can be legally performed and characterizing Poss (Dap); (FO) successor state axioms describing how fluents change between situations (Dss); (FO) unique name axioms for actions and (FO) domain closure axioms on action types (Duna); (SO) unique name and domain closure axioms for object constants (Dcoa); and (FO) axioms describing the initial configuration of the world (D0), which we assume finite
We have proposed a decidable framework for verifying agents with bounded beliefs operating in infinite state domains
Summary
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]. For bounded theories, by iterating progression steps we obtain a “computationally grounded” model of agents [52], in the sense that such a model captures how the belief states of agents are generated and updated from the action theory, which describes what is true (according to the agent) and how this evolves as actions are performed With this result on progression in place, we investigate the verification of online executions of agents. We introduce a language for expressing temporal properties of online executions (a first-order variant of the μ-calculus), and show our main result, i.e., that verification of such properties over bounded action theories is decidable.
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