Asymptotic Probabilities of Languages with Generalized Quantifiers

  title={Asymptotic Probabilities of Languages with Generalized Quantifiers},
  author={Guy Fayolle and St{\'e}phane Grumbach and Christophe Tollu},
W e study the impact of adding certain families of generalized quantifiers to first-order logic (FO) on the asymptotic behavior of sentences. All our results are stated and proved for languages disallowing free variables in the scope of generalized quantifiers. For a class K of finite structures closed under isomorphism, the quantifier QK is said to be strongly monotonic, sm, i f membership in the class is preserved under a loose f o m of extensions. Our first theorem (0/1 law for FO with any… CONTINUE READING

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