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Abstract: We 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, if membership in the class is preserved under a loose form of extensions. Our first theorem (0/1 law for FO with any set... (Update)
Context of citations to this paper: More
...the cardinality of R is bigger than the cardinality of S. The asymptotic probability of the above query is 1 2 . The result follows from [FGT93], where it is shown that first order sentences with limited Rescher s quantifiers (expressing cardinality comparison) have asymptotic...
...of first order logic by Lindstrom quantifiers. Such extensions were also considered, from the point of view of 0 1 laws by Fayolle et al. [8], where a sufficient condition was established on a quantifier Q, for a restricted fragment of the logic FO[Q] to have a 0 1 law. We...
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BibTeX entry: (Update)
G. Fayolle, S. Grumbach, and C. Tollu. Asymptotic probabilities of languages with generalized quantifiers. In Proc. IEEE Symp. on Logic in Computer Science, pages 199--207, June 1993. http://citeseer.ist.psu.edu/fayolle94asymptotic.html More
@inproceedings{ fayolle93asymptotic,
author = "Guy Fayolle and Stephane Grumbach and Christophe Tollu",
title = "Asymptotic Probabilities of Languages with Generalized Quantifiers",
booktitle = "Logic in Computer Science",
pages = "199-207",
year = "1993",
url = "citeseer.ist.psu.edu/fayolle94asymptotic.html" }
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