Circular languages

Abstract
In this paper we investigate two purely syntactical notions ofcircularity, which we call ``self-application'''' and ``self-inclusion.'''' Alanguage containing self-application allows linguistic items to beapplied to themselves. In a language allowing for self-inclusion thereare expressions which include themselves as a proper part. We introduceaxiomatic systems of syntax which include identity criteria andexistence axioms for such expressions. The consistency of these axiomsystems will be shown by providing a variety of different models –these models being our circular languages. Finally we will show what apossible semantics for these circular languages could look like.
Keywords application  circularity  non-well-founded sets  paradox  syntax
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