ACM Transactions on Computer Systems (TOCS)
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LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
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Artificial Intelligence
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Proceedings of the fourth international joint conference on Autonomous agents and multiagent systems
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Propositional independence: formula-variable independence and forgetting
Journal of Artificial Intelligence Research
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IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
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IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
On the semantics of knowledge update
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Forgetting and uniform interpolation in large-scale description logic terminologies
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
On first-order definability and computability of progression for local-effect actions and beyond
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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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 Γ and a set of observable variables Oi for each agent i, we show that the notion of agent i knowing a formula ϕ can be defined as a weakest sufficient condition of ϕ over Oi under Γ 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.