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. (shrink)

VSK logic is a family multi-modal logics for reasoning about the information properties of computational agents situated in some environment. Using VSK logic, we can represent what is objectively true of the environment, the information that is visible, or knowable about the environment, information the agent perceives of the environment, and finally, information the agent actually knows about the environment. The semantics of VSK logic are given in terms of a general, automata-like model of agents. In this paper, we prove (...) completeness for an axiomatisation of VSK logic, and present correspondence results for a number of VSK interaction axioms in terms of the architectural properties of the agent that they represent. The completeness proof is novel in that we are able to prove completeness with respect to the automata-like semantics. In this sense, VSK logic is said to be computationally grounded. We give an example to illustrate the formalism, and present conclusions and issues for further work. (shrink)

Specifying and implementing dynamical systems with the situation calculus.