Circular Languages

Authors:
Hannes Leitgeb;Alexander Hieke
Affiliations:
Department of Philosophy, University of Salzburg, Franziskanergasse 1, A-5020 Salzburg, Austria/ E-mail: hannes.leitgeb@sbg.ac.at;Department of Philosophy, University of Salzburg, Franziskanergasse 1, A-5020 Salzburg, Austria/ E-mail: alexander.hieke@sbg.ac.at
Venue:
Journal of Logic, Language and Information
Year:
2004

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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.