This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective.

本文探讨了逻辑敏感性和位串语义之间的对立相互作用。位串语义是一种组合技术，用于表示出现在逻辑图中的公式，而逻辑敏感性意味着这样的图不仅取决于所涉及的公式，还取决于解释它们所依据的逻辑。这两个主题已经在逻辑几何中得到了广泛的研究，因此它们本身也得到了很好的理解。然而，它们相互作用的具体细节却要复杂得多。特别是，本文描述了位串和逻辑敏感性之间优雅而自然的交互，当位串被视为纯粹的组合实体时，这是完全有意义的。然而，语义'！），这种交互似乎没有一个完整且同样自然的对应物。该论文描述了解决这种情况的一些尝试，但最终发现所有这些尝试都不尽如人意。因此，目前，从语义（而不仅仅是组合）角度捕获位串和逻辑敏感性之间的交互仍然是一个悬而未决的问题。