An Algebraic Structuring of Epistemic States for BDI Agents in Uncertain Environments

Charles A. N. Costa, Marlo Souza, Célia Ghedini Ralha

Keywords: Belief-Desire-Intention, epistemic states, uncertain beliefs, algebra

TL;DR: Structuring the belief revision operator of CAN+, an extension of CAN language for BDI agents, as an abelian group, with suggested applications.

Abstract: Reasoning about uncertainty is challenging for the design of Belief-Desire-Intention (BDI) agents. In dynamic, faulty, noisy, and partially observable environments, agents must frequently make decisions under uncertain beliefs. To address this ongoing challenge, the literature proposes several approaches, such as the use of stratified belief bases, as in the CAN+ framework. CAN+ provides a robust formal framework for agents to store and revise beliefs as weighted formulas. Nevertheless, reasoning about weighted formulas beyond entailment can be difficult. To better address these difficulties, we contribute an algebraic approach to reasoning about uncertain beliefs, focusing on stratified (or weighted) belief bases within the CAN+ framework and on a belief revision operator for updating such belief bases. In addition, we suggest modifications to the syntactic revision operator of CAN+ to structure an algebraic group, thus facilitating reasoning about the properties of systems implemented in CAN+. By providing a strong algebraic basis for the language, this work facilitates simplification rules and algorithms for reasoning over uncertain beliefs related to belief updating. To illustrate these concepts, we present the application of CAN+ reasoning for solving equations and supporting regression planning with the backward search algorithm in the vacuum world scenario.

Area: Representation and Reasoning (RR)

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Submission Number: 821