This paper is about the concept of semantically closed languages. Roughly speaking, those are languages which can name their own sentences and apply to them semantic predicates, such as the truth or satisfaction predicates. Hence, they are “self-referential languages,” in the sense that they are capable of producing sentences about themselves or other sentences in the same language. In section one, we introduce the concept informally; in section two, we provide the formal definition of first-order semantically closed languages, which is the Tarskian definition with some technical modifications. Then, we construct a semantic for this kind of language, and prove that the language is indeed semantically closed (according to Definition 1). Finally, we discuss whether the logic underlying the construction is classical, and future goals of this research.

本文讨论的是语义封闭语言的概念。粗略地说，这些语言可以命名自己的句子并向其应用语义谓词，例如真相或满足谓词。因此，它们是“自指语言”，因为它们能够产生关于自己的句子或同一语言中的其他句子。在第一节中，我们非正式地介绍了这个概念；在第二节中，我们提供了一阶语义封闭语言的形式定义，这是经过一些技术修改的 Tarskian 定义。然后，我们为这种语言构造一个语义，并证明该语言确实是语义封闭的（根据定义1）。最后，我们讨论了该构建背后的逻辑是否经典，以及本研究的未来目标。