Belief Shadowing

Adapting beliefs to new circumstances, like belief change, update, revision or merging, typically requires deep and/or complex adjustments of belief bases even when adaptations happen to be transient. We present a novel, lightweight and tractable approach to a new kind of beliefs’ interference which we call belief shadowing. Put simply, it is a transient swap of beliefs when part of one belief base is to be shadowed by another belief base representing new observations and/or beliefs of superior agents/teams. In this case no changes to belief bases are needed. This substantially improves the performance of systems based on doxastic reasoning. We ensure tractability of our formal framework, what makes it suitable for real-world applications. The presented approach is based on a carefully chosen four-valued paraconsistent logic with truth values representing truth, falsity, incompleteness and inconsistency. Moreover, potentially undesired or forbidden conclusions are prevented by integrity constrains together with their shadowing machinery. As an implementation environment we use \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\hbox {QL}^{\mathrm{Bel}}$$\end{document}, a recently developed four-valued query language based on the same underlying logic and providing necessary reasoning tools. Importantly, the shadowing techniques are general enough to be embedded in any reasoning environment addressing related phenomena.