Variable Forgetting in Reasoning about Knowledge

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Title Variable Forgetting in Reasoning about Knowledge
Author Su, Kaile; Sattar, Abdul; Lv, Guanfeng; Zhang, Yan
Journal Name The Journal of Artificial Intelligence Research
Year Published 2009
Place of publication United States
Publisher A I Access Foundation, Inc
Abstract In this paper, we investigate knowledge reasoning within a simple framework called knowledge structure. We use variable forgetting as a basic operation for one agent to reason about its own or other agents\' knowledge. In our framework, two notions namely agents\' observable variables and the weakest sufficient condition play important roles in knowledge reasoning. Given a background knowledge base and a set of observable variables for each agent, we show that the notion of an agent knowing a formula can be defined as a weakest sufficient condition of the formula under background knowledge base. Moreover, we show how to capture the notion of common knowledge by using a generalized notion of weakest sufficient condition. Also, we show that public announcement operator can be conveniently dealt with via our notion of knowledge structure. Further, we explore the computational complexity of the problem whether an epistemic formula is realized in a knowledge structure. In the general case, this problem is PSPACE-hard; however, for some interesting subcases, it can be reduced to co-NP. Finally, we discuss possible applications of our framework in some interesting domains such as the automated analysis of the well-known muddy children puzzle and the verification of the revised Needham-Schroeder protocol. We believe that there are many scenarios where the natural presentation of the available information about knowledge is under the form of a knowledge structure. What makes it valuable compared with the corresponding multi-agent S5 Kripke structure is that it can be much more succinct.
Peer Reviewed Yes
Published Yes
Alternative URI http://dx.doi.org/10.1613/jair.2750
Copyright Statement Copyright 2009. A I Access Foundation, Inc. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
Volume 35
Page from 677
Page to 716
ISSN 1076-9757
Date Accessioned 2010-04-30
Date Available 2010-08-25T07:03:00Z
Language en_AU
Research Centre Institute for Integrated and Intelligent Systems
Faculty Faculty of Science, Environment, Engineering and Technology
Subject Artificial Intelligence and Image Processing
URI http://hdl.handle.net/10072/30908
Publication Type Journal Articles (Refereed Article)
Publication Type Code c1

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