| 摘要: |
| 首先建立了一种多Agent信念逻辑MBL(multi-agentbelieflogic),在经典信念逻辑基础上增加了普遍信念算子和公共信念算子,给出MBL的Kripke语义与广义Aumann语义,讨论了两者的等价性,证明了MBL对于上述两种语义的可靠性和完备性.其次,建立了一种多Agent概率信念逻辑MPBL(multi-agentprobabilisticbelieflogic),通过在广义Aumann语义基础上引入概率空间,给出了MPBL的概率Aumann语义,证明了它的可靠性,并给出MPBL的一些推论. |
| 关键词: 信念逻辑 Kripke语义 广义Aumann语义 概率信念逻辑 概率Aumann语义 多Agent系统 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金资助项目(69973023;69733020);黑龙江省自然科学基金资助项目(F00-04) |
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| A Multi-Agent Belief Logic and Its Generalization with Probability |
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CAO Zi ning,DONG Hong bin,SHI Chun yi
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| Abstract: |
| In this paper, a multi-agent belief logic named MBL (multi-agent belief logic) is presented firstly. Based on the classical belief logic, MBL is added into the modal operators of every-belief and common belief. Then the Kripke semantics and generalized Aumann semantics of MBL are given, the equivalence of the two semantics, the soundness and completeness of MBL about the two semantics are proved. Secondly, a multi agent probabilistic belief logic named MPBL (multi-agent probabilistic belief logic) is presented. By introducing the probability space on generalized Aumann model, the probabilistic Aumann semantics of MPBL are given, and its soundness about generalized Aumann semantics is proved. At last, some corollaries of MPBL are given. |
| Key words: belief logic Kripke semantics generalized Aumann semantics probabilistic belief logic probabilistic Aumann semantics MAS （multi agent system） |
