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Summary: Expressive power and complexity of a logic with
quantifiers that count proportions of sets
Argimiro Arratia
Dpto. de Matem´atica Aplicada
Facultad de Ciencias
Universidad de Valladolid
Valladolid 47005, Spain
arratia@mac.uva.es
Fax: +34 - 983423013
Carlos E. Ortiz
Department of Mathematics
and Computer Science
Arcadia University
450 S. Easton Road,
Glenside, PA 19038-3295, U.S.A.
ortiz@arcadia.edu
Abstract
We present a second order logic of proportional quantifiers, SOLP, which is
essentially a first order language extended with quantifiers that act upon second
order variables of a given arity r, and count the fraction of elements in a subset
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