Summary: Syntactic approximations to computational
and Carlos E. Ortiz2
Dpto. de Matem´atica Aplicada, Facultad de Ciencias, Universidad de Valladolid,
Valladolid 47005, Spain, firstname.lastname@example.org,
Department of Mathematics and Computer Science, Arcadia University, 450 S.
Easton Road, Glenside, PA 19038-3295, U.S.A. email@example.com
Abstract. We present a formal syntax of approximate formulas suited
for the logic with counting quantifiers SOLP. This logic was studied by
us in  where, among other properties, we showed: (i) In the presence of
a builtin (linear) order, SOLP can describe NPcomplete problems and
fragments of it capture classes like P and NL; (ii) weakening the ordering
relation to an almost order we can separate meaningful fragments, using
a combinatorial tool adapted to these languages.
The purpose of the approximate formulas presented here, is to provide a
syntactic approximation to logics contained in SOLP with built-in order,
that should be complementary of the semantic approximation based on