Knowledge Spaces with Arbitrarily High Rank
Knowledge Spaces with Arbitrarily High Rank
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具有任意高等级的知识空间
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
D. Samet
中科院分区：
文献类型：
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作者：
A. Heifetz;D. Samet
摘要概率信念空间类（Harsanyi，1967-68，Man. Sci.，14，159-182，320-324，486-502）包含一个泛空间，每一个其他的信念空间可以通过信念态射以唯一的方式映射到其中。我们证明了在知识空间类中不存在类似的泛空间。为了证明这一点，我们定义了知识空间的秩，这是空间中最复杂的知识描述的有序性。然后，我们表明，知识空间可以映射的知识态射只有空间的更高或相等的秩。我们构造任意高秩的知识空间，证明不存在普适空间。经济文献分类号：D80、D82。
Abstract The class of probabilistic belief spaces (Harsanyi, 1967–68, Man. Sci. , 14, 159–182, 320–324, 486–502) contains a universal space , into which every other belief space can be mapped in a unique way by a belief morphism. We show that there is no analogous universal space in the class of knowledge spaces. To show this we define the rank of a knowledge space, which is the ordinality of the most complicated descriptions of knowledge in the space. We then show that a knowledge space can be mapped by a knowledge morphism only to spaces of higher or equal rank. We construct knowledge spaces for arbitrarily high rank, demonstrating that there is no universal space. Journal of Economic Literature Classification Numbers: D80, D82.