An exclusive disjunction is true when exactly one of the disjuncts is true. In the case of the familiar binary exclusive disjunction, we have a formula occurring as the first disjunct and a formula occurring as the second disjunct, so, if what we have is two formula-tokens of the same formula-type—one formula occurring twice over, that is—the question arises as to whether, when that formula is true, to count the case as one in which exactly one of the disjuncts is true, counting by type, or as a case in which two disjuncts are true, counting by token. The latter is the standard answer: counting by tokens. James McCawley once suggested that, when the exclusively disjunctive construction in natural language (well, in English at least) is at issue, the construction should be treated as involving a multigrade connective whose semantic treatment is sensitive to the set of disjuncts rather than the corresponding multiset. Without any commitment as to whether there actually is such a construction (in English), and conceding that for obvious pragmatic reasons such ‘repeated disjunct’ cases would be at best highly marginal, we note that for the binary case, this requires a nonstandard answer—count by type rather than by token—to the earlier question, and thus, an idempotent exclusive disjunction connective. Section 2 explores that idea and Section 3, a further idempotent variant for which it is the propositions expressed by the disjuncts, rather than the disjuncts themselves, that get counted once only in the case of repetitions. Sections 1 and 4 respectively set the stage for these investigations and conclude the discussion (after noting an intimate connection between the logic of Section 3 and the modal logic S5). More detailed considerations of points arising from the discussion but otherwise in danger of interrupting the flow are deferred to a ‘Longer Notes’ appendix at the end (Section 5.)

当正好有一个析取为真时，排他析取为真。在熟悉的二元互斥析取的情况下，我们有一个作为第一个析取出现的公式和一个作为第二个析取出现的公式，所以，如果我们有两个相同公式类型的公式标记——一个公式出现两次结束，即——问题在于，当该公式为真时，是将这种情况计算为其中一个析取项中的一个为真，按类型计算，还是计算为两个析取项为真的情况，计算通过令牌。后者是标准答案：按代币计数。James McCawley 曾经建议，当自然语言（至少在英语中）中的完全分离式结构存在争议时，一组析取项而不是相应的多重集. 没有任何关于是否真的有这样的结构（英文）的承诺，并承认出于明显的务实原因，这种“重复分离”的情况充其量是非常边缘的，我们注意到对于二元情况，这需要一个非标准的答案- 按类型而不是按标记计数 - 到前面的问题，因此，一个幂等的排他析取连接词。第 2 节探讨了这个想法，第 3 节是一个进一步的幂等变体，它是由析取项表达的命题，而不是析取项本身，仅在重复的情况下被计数一次。第 1 节和第 4 节分别为这些调查奠定了基础并结束了讨论（在注意到第 3 节的逻辑和模态逻辑S5）。对讨论中提出但有中断流程危险的要点的更详细考虑被推迟到末尾的“更长的注释”附录（第 5 节）。