Languages with self-reference I: Foundations

It is argued that a proper treatment of cognitive notions such as beliefs and concepts should allow broad and consistent expression of syntax and semantics, and that this in turn depends on self-reference. A theory of quotation and unquotation is presented to this end that appears to make unnecessary the usual hierarchical and non-first-order constructions for these notions. In the current paper (Part I) the underlying theory is presented; a sequel will treat in more detail the applications to cognition.