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A zero-one law for random sentences in description logics

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Mathematics and Computer Science

Part of the book series: Trends in Mathematics ((TM))

Abstract

We consider the set of sentences in a decidable fragment of first order logic, restricted to unary and binary predicates, expressed on a finite set of objects. Probability distributions on that set of sentences are defined and studied. For large sets of objects, it is shown that under these distributions, random sentences typically have a very particular form, and that all monotone symmetric properties of these random sentences have a probability close to 0 or 1.

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Author information

Authors and Affiliations

  1. UFR Math-Info, 45 rue des Saints-Pères, 75270, Paris Cedex 06, France

    Bernard Ycart

  2. LRI, UMR 8623 CNRS, University of Paris Sud, 91405, Orsay Cedex, France

    Marie-Christine Rousset

Authors
  1. Bernard Ycart
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  2. Marie-Christine Rousset
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Editor information

Editors and Affiliations

  1. Bâtiment Descartes, Université de Versailles-St-Quentin PRISM, 45 avenue des Etats-Unis, 78035, Versailles, Cedex, France

    Danièle Gardy

  2. Département de Mathématiques Bâtiment Fermat, Université de Versailles-St-Quentin, 45 avenue des Etats-Unis, 78035, Versailles, Cedex, France

    Abdelkader Mokkadem

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© 2000 Springer Basel AG

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Ycart, B., Rousset, MC. (2000). A zero-one law for random sentences in description logics. In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_28

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  • DOI: https://doi.org/10.1007/978-3-0348-8405-1_28

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9553-8

  • Online ISBN: 978-3-0348-8405-1

  • eBook Packages: Springer Book Archive

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