区分计数：论香农信息论的概念基础
Counting Distinctions: On the Conceptual Foundations of Shannon's Information Theory
摘要：
范畴逻辑已经表明，现代逻辑本质上是子集逻辑（或“子子集”）。划分是子集的对偶，因此存在划分的对偶逻辑，其中“区别”[来自全域U的不同元素（u，u '）的有序对]是“元素”的对偶。在子集中的元素类似于U上的划分p，从而进行区分，即，如果u和u'在p的不同块中。子集逻辑通过将（拉普拉斯）概率作为有限论域的每个子集事件的归一化大小而导致有限概率论。划分逻辑中的类似步骤是将划分的区分数分配给划分，该区分数由来自有限论域的有序对|UxU|的总数归一化。这就产生了划分的“逻辑熵”概念和“逻辑信息论”。“逻辑理论直接计算分区中的（标准化）区别数量，而香农的理论给出了做出这些相同区别所需的二进制分区的平均数量。因此，逻辑理论被看作是为香农的理论提供了一个概念性的基础上的逻辑概念的“区别”。“（即将发表于《综合》）
英文摘要：
Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u') from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition p on U making a distinction, i.e., if u and u' were in different blocks of p. Subset logic leads to finite probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |UxU| from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions." (forthcoming in Synthese)
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