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Leitgeb, Hannes; Hieke, Alexander (December 2004): Circular Languages. In: Journal of Logic, Language and Information, Vol. 13, No. 3: pp. 341-371
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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.