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Modal Expressivity and Definability over Sets

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Logic, Rationality, and Interaction (LORI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5834))

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Abstract

The link between modal logic and non-well-founded sets has been shown by P. Aczel [1988], and systematically by J. Barwise and L. Moss [1996]. A. Baltag [1998] also proved some important theorems about characterizing sets by modal sentences. The aim of this paper is to explore the relationship between modal logic and sets more deeply in the expressive power of modal languages and modal definability over sets. Let’s consider both basic and infinitary modal languages.

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References

  1. Aczel, P.: Non-Well-Founded Sets. Stanford CSLI publications (1988)

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  2. Baltag, A.: STS: A Structural Theory of Sets. Ph.D. dissertation, Indiana University (1998)

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  3. Blackburn, P., de Rijke, M., de Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)

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  4. Segerberg, K.: An Essay in Classical Modal Logic. Filosofiska Studier 13, University of Uppsala (1971)

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  5. Jech, T.: Set Theory. Springer, Heidelberg (2003)

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  6. Barwise, J., Moss, L.: Vicious Circles: On the Mathematics of Non-Well-Founded Phenomena. CSLI publications, Stanford (1996)

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Author information

Authors and Affiliations

  1. Institute for Modern Logic, Central University of Finance and Economics, Beijing, China, 100081

    Jing Shi

Authors
  1. Jing Shi
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Editors and Affiliations

  1. Institute of Logic and Intelligence, Southwest University, 2, Tiansheng Road, 400715, Chongqing, China

    Xiangdong He

  2. Philosophy Department, University of Maryland, Institute for Advanced Computer Studies (UMIACS), 20742, College Park, MD, USA

    John Horty

  3. Center for Logic and Philosophy of Science, Tilburg University, Dante Building, 5000, Tilburg, LE, The Netherlands

    Eric Pacuit

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© 2009 Springer-Verlag Berlin Heidelberg

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Shi, J. (2009). Modal Expressivity and Definability over Sets. In: He, X., Horty, J., Pacuit, E. (eds) Logic, Rationality, and Interaction. LORI 2009. Lecture Notes in Computer Science(), vol 5834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04893-7_30

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  • DOI: https://doi.org/10.1007/978-3-642-04893-7_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04892-0

  • Online ISBN: 978-3-642-04893-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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