Progression and Verification of Situation Calculus Agents with Bounded Beliefs

Abstract

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.

Bounded situation calculus action theories

“…The form of boundedness studied in that case requires that the number of object tuples that the agent thinks may belong to any given fluent be bounded. In [30,29], instead, it is only required that number of distinct tuples entelied to belong to a fluent is bounded, while the number of tuples that are in the extension of a fluent in some model of the theory need not be bounded. More work is needed to fully reconcile these meta-theoretic and language-theoretic approaches.…”

“…Example 1. Consider a warehouse where items are moved around by a robot (a similar example is formalized in [30]). There are k storage locations where items can be stored.…”

“…More recently, work closely related to ours [27,28,30,29] has shown that one gets robust decidability results for temporal verification of situation calculus action theories under the assumption that in every situation the number of object tuples forming the extension of each fluent is bounded by a constant. In particular, [27] introduced bounded situation calculus basic action theories; [27] however, assumes standard names for the object domain and, more significantly, disallows quantification across situations in the verification language.…”

Knowledge-based programs as succinct policies for partially observable domains

“…The least we can require for a fragment of Golog to be acceptable for building knowledge-based programs on it is that it is decidable, so that branching conditions can be evaluated and a knowledge-based program can always be executed. A few attempts to identify decidable classes of epistemic situation calculus theories have been made [36,30,31,74], but without addressing knowledge-based programming.…”

Tools for Strategic Decision Support in Energy Sector Based on Situation Management and Semantic Modeling

“…Thus, in [3] the authors discuss the possibility to employ a new approach to deriving new knowledge in multi-agent systems to eventually let an agent act with available data only, instead of inquiring knowledge from all agents. In paper [4] they describe the approach to verify temporal properties of agents possessing incomplete knowledge on the world and using situation calculus bounded action theories. Besides, in [5] the researchers proposed to employ situation calculus and event calculus in the general theory of steady models and answer set programming.…”