Abstract
In this paper, we present a logic system for probabilistic belief named PBL, which expands the language of belief logic by introducing probabilistic belief. Furthermore, we give the probabilistic Aumann semantics of PBL. We also list some valid properties of belief and probabilistic belief, which form the deduction system of PBL. Finally, we prove the soundness and completeness of these properties with respect to probabilistic Aumann semantics.
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References
Hintikka J. Knowledge and Belief, Ithaca, NY: Cornell University Press, 1962.
Aumann R J. Agreeing to disagree.Ann. Stat, 1976, 4(6): 1236–1239.
Fudenberg D, Tirole J. Game Theory. Cambridge, Massachusetts: The MIT Press, 1991.
Fagin R, Halpern J Y, Moses Y, Vardi M Y. Reasoning about Knowledge. Cambridge, Massachusetts: The MIT Press, 1995.
Fagin R, Halpern J Y. Reasoning about knowledge and probability.J. ACM, 1994, 41(2): 340–367.
Halpern J Y, Moses Y. Knowledge and common knowledge in a distributed environment.J. ACM, 1990, 37(3): 549–587.
Levesque H J. A logic of implicit and explicit belief.AAAI-84, Austin, TX, pp.198–202.
Konolige K. A Deduction Model of Belief. Pitman Publishing, 1986.
Rao A S, Georgeff M P. Modeling rational agents within a BDI-architecture. InPrinciples of Knowledge Representation and Reasoning: Proc. The Second International Conference (KR'91) Allen J, Fikes R, Sandewall E (eds.), California: Morgan Kaufmann Publishers, 1991, pp.473–484.
Rao A S, Georgeff M P. An abstract architecture for rational agents. InPrinciples of Knowledge Representation and Reasoning: Proc. The Third International Conference (KR'92), Nebel B, Rich C, Swartout W (eds.), California: Morgan Kaufmann Publishers, 1992, pp. 439–449.
Wooldridge M, Jennings N R. Intelligent agents: Theory and practice.The Knowledge Engineering Review, 1995, 10(2): 115–152.
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This work is supported by the National Natural Science Foundation of China under Grant Nos. 60203028, 60173011, 69833020.
CAO ZiNing received the Ph.D. degree in computer science from Tsinghua University in 2001. Now he is a postdoctoral fellow at the Institute of Software, Chinese Academy of Sciences. His main research interests include logic in computer science and concurrency theory.
SHI ChunYi is a professor for computer science at Tsinghua University. His main research interests include logic in artificial intelligence, machine learning and multi-agent system.
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Cao, Z., Shi, C. Probabilistic belief logic and its probabilistic Aumann semantics. J. Comput. Sci. & Technol. 18, 571–579 (2003). https://doi.org/10.1007/BF02947116
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DOI: https://doi.org/10.1007/BF02947116