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Circular Languages

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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.

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References

  • Aczel, P., 1980, "Frege structures and the notions of proposition, truth and set," pp. 31–59 in The Kleene Symposium, J. Barwise, H.J. Keisler, and K. Kunen, eds., Amsterdam: North-Holland.

    Google Scholar 

  • Aczel, P., 1988, Non-Well-Founded Sets, CSLI Lecture Notes 14, Stanford, CA: CSLI.

    Google Scholar 

  • Barendregt, H., Bunder, M., and Dekkers, W., 1993, "Systems of illative combinatory logic complete for first-order propositional and predicate calculus," Journal of Symbolic Logic 58, 769–788.

    Google Scholar 

  • Barwise, J. and Etchemendy, J., 1987, The Liar.An Essay on Truth and Circularity,NewYork: Oxford University Press.

    Google Scholar 

  • Barwise, J. and Moss, L., 1996, Vicious Circles, CSLI Lecture Notes 60, Stanford, CA: CSLI.

    Google Scholar 

  • Bealer, G., 1982, Quality and Concept, Oxford: Clarendon Press.

    Google Scholar 

  • Feferman, S., 1984, "Toward useful type-free theories I," Journal of Symbolic Logic 49, 75–111.

    Google Scholar 

  • Gupta, A. and Belnap, N., 1993, The Revision Theory of Truth, Cambridge, MA: MIT Press.

    Google Scholar 

  • Halbach, V., 1996, Axiomatische Wahrheitstheorien, Berlin: Akademie-Verlag.

    Google Scholar 

  • Hindley, J.R. and Seldin, J.P., 1986, Introduction to Combinators and ë -Calculus, Cambridge: Cambridge University Press.

    Google Scholar 

  • Lloyd, J.W., 1987, Foundations of Logic Programming, 2nd edition, Berlin; Springer-Verlag.

    Google Scholar 

  • Tarski, A., 1935, "Der Wahrheitsbegriff in den formalisierten Sprachen," Studia Philosophica 1, 261–405. English translation in: Tarski, A., Logic, Semantics, Metamathematics, 2nd edition, Hackett, Indianapolis, pp. 152–278.

    Google Scholar 

  • Turner, R., 1987, "A theory of properties," Journal of Symbolic Logic 52, 455–472.

    Google Scholar 

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Authors and Affiliations

  1. Department of Philosophy, University of Salzburg, Franziskanergasse 1, A-5020, Salzburg, Austria

    Hannes Leitgeb & Alexander Hieke

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  1. Hannes Leitgeb
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  2. Alexander Hieke
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Leitgeb, H., Hieke, A. Circular Languages. Journal of Logic, Language and Information 13, 341–371 (2004). https://doi.org/10.1023/B:JLLI.0000028335.19112.1d

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  • DOI: https://doi.org/10.1023/B:JLLI.0000028335.19112.1d

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