Group Belief
Group Belief
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团体信念
DOI：
10.1007/978-3-030-44638-3_1
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Yì N. Wáng
中科院分区：
文献类型：
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作者：
Thomas Ågotnes;Yì N. Wáng
虽然群体知识概念的逻辑形式化，如共同知识和分布式知识，在文献中得到了相当多的关注，但大多数方法都是基于模态逻辑的，群体信念概念得到的关注要少得多。本文系统地研究了在关于信念性质的不同假设下群体信念的标准概念。特别是，我们针对群体信仰的不同标准定义绘制出信仰属性的保存（缺乏）。事实证明，所谓的群体信仰往往不是真正的信仰，也就是说，它不具备信仰的属性。事实上，即使是所谓的群体知识有时也不是真正的知识。例如，在信念具有KD45属性的共同假设下，无论是共同信念（不满足否定自省公理5）还是分布信念（不满足一致性公理D）都不是真正的信念。关于分布式知识的逻辑公理化的合理性，在文献中存在一些混淆，这与提到的缺乏保存有关。在本文中，我们还给出了KD45在有和没有共同信念的分布式信念下的健全和完全公理化的详细完备性证明。
While logical formalizations of group notions of knowledge such as common and distributed knowledge have received considerable attention in the literature, most approaches being based on modal logic, group notions of belief have received much less attention. In this paper we systematically study standard notions of group belief under different assumptions about the properties of belief. In particular, we map out (lack of) preservation of belief properties against different standard definitions of group belief. It turns out that what is called group belief most often is not actually belief, i.e. does not have the properties of belief. In fact, even what is called group knowledge is sometimes not actually knowledge either. For example, under the common assumption that belief has the KD45 properties, neither common belief (does not satisfy the negative introspection axiom 5) nor distributed belief (does not satisfy the consistency axiom D) are not actually belief. There has been some confusion in the literature regarding soundness of proposed axiomatizations of logics with distributed knowledge, related to the mentioned lack of preservation. In this paper we also present detailed completeness proofs of sound and complete axiomatizations of KD45 with distributed belief, both with and without common belief.