有限上下文超图强制的伪上下文
Pseudocontexts forced by finite context hypergraphs
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中文总结 AI 辅助
该研究定义了伪上下文，给出其精确有限测试，在三维下得到实、复示例，确定复数域上每组最少结果数为2、实数域上为3。
中文摘要 AI 辅助
上下文是一组互斥结果的完整集合，其概率之和为1。我们将伪上下文定义为两个不相交的组，每组内不存在互斥对，但仅因上下文的重叠方式，它们的总概率必须相等。我们给出该性质的精确有限测试，并证明该等式与所选坐标和概率模型无关。在三维下应用该测试，我们得到一个含15个结果、每组3个的实示例，以及一个含20个结果、每组2个的复示例。根据此定义，在复数域上每个目标组的最少结果数为2，在实数域上为3。
英文摘要
A context is a complete set of mutually exclusive outcomes whose probabilities sum to one. We define a pseudocontext as two disjoint groups, with no mutually exclusive pair within either group, whose total probabilities must nevertheless be equal solely because of how the contexts overlap. We give an exact finite test for this property and show that the equality is independent of the chosen coordinates and probability model. Applying the test in three dimensions, we obtain a 15-outcome real example with groups of three and a 20-outcome complex example with groups of two. Under this definition, the sharp minimum number of outcomes in each target group is two over the complex field and three over the real field.
