This paper develops a formal logic for guises based on the work of Héctor-Neri Castañeda, who understood relations from an internalist viewpoint, following Leibniz. We introduce a syntax, model theory, and proof theory for an intensional logic in which guises (taken as bundles of properties equipped with intention) serve as primary semantic objects. The system integrates (i) a Leibnizian containment semantics for singular truths, (ii) an intentional operator that captures internal relations among guises, and (iii) a modal layer for possibility and necessity modeled as maximally consistent closures. We establish core metatheoretic results (e.i. soundness and canonical-model completeness sketches) and analyze hyperintensional phenomena such as substitution failure in intentional contexts, quasi-indexicality, and de se reference. We compare the framework to classical intensional semantics (Montague), property theory (Bealer), hyperintensional logics (Fine), situation semantics (Barwise and Perry), and to the Leibniz program for a calculus of concepts. The result is a selfcontained formal framework that demonstrates that relations are not external causal links but intentional internal structures encoded in the guises through which agents and objects are conceived: i.e., they are perspectives.

翻译：本文基于Héctor-Neri Castañeda的工作（其沿袭莱布尼茨的内在主义视角理解关系），发展了一套针对“外观”（guises）的形式逻辑。我们引入了内涵逻辑的语法、模型论和证明论，其中外观（被视作具有意向性的属性束）作为基本语义对象。该体系整合了：(i) 对单称真命题的莱布尼茨式包含语义，(ii) 捕获外观间内在关系的意向算子，以及(iii) 以最大一致闭包建模可能性与必然性的模态层。我们建立了核心元定理（如可靠性与典范模型完备性纲要），并分析了意向语境中的替换失效、准索引性及自我指称等超内涵现象。我们将该框架与经典内涵语义学（Montague）、属性理论（Bealer）、超内涵逻辑（Fine）、情境语义学（Barwise与Perry）以及莱布尼茨的概念演算纲领进行比较。最终呈现的是一个自洽的形式框架，论证了关系并非外部因果联结，而是编码于外观中的意向性内在结构——通过这些结构，行动者与对象得以被构想：即，它们是视角。