This paper develops a theory of propositional identity which distinguishes necessarily equivalent propositions that differ in subject-matter. Rather than forming a Boolean lattice as in extensional and intensional semantic theories, the space of propositions forms a non-interlaced bilattice. After motivating a departure from tradition by way of a number of plausible principles for subject-matter, I will provide a Finean state semantics for a novel theory of propositions, presenting arguments against the convexity and nonvacuity constraints which Fine (Journal of Philosophical Logic, 4545, 199–226 13, 14, 15) introduces. I will then move to compare the resulting logic of propositional identity (PI¹) with Correia’s (The Review of Symbolic Logic, 9, 103–122 9) logic of generalised identity (GI), as well as the first degree fragment of Angell’s (2) logic of analytic containment (AC). The paper concludes by extending PI¹ to include axioms and rules for a subject-matter operator, providing a much broader theory of subject-matter than the principles with which I will begin.

本文发展了命题同一性理论，该理论区分了主题不同的必然等价命题。命题空间不是像外延语义理论和内涵语义理论那样形成布尔格，而是形成非交错的二格。在通过主题的一些似是而非的原则激励背离传统之后，我将为新的命题理论提供 Finean 状态语义，提出反对 Fine ( Journal of Philosophical Logic , 4545)的凸性和非空性约束的论据, 199–226 13, 14, 15) 介绍。然后，我将比较命题同一性（PI ¹）的结果逻辑与 Correia 的（符号逻辑评论，9, 103–122 9) 广义同一性 (GI) 逻辑，以及 Angell (2) 分析遏制 (AC) 逻辑的一级片段。本文最后将 PI ¹扩展为包含主题运算符的公理和规则，提供了比我将开始的原则更广泛的主题理论。