 
Summary: Results from MathSciNet: Mathematical Reviews on the Web
c Copyright American Mathematical Society 2006
MR2095228 (2005f:68050) 68Q19 03B48 03C13 68Q15
Arratia, Argimiro (YVSBOL); Ortiz, Carlos E.
Approximating the expressive power of logics in finite
models. (English. English summary)
LATIN 2004: Theoretical informatics, 540556, Lecture Notes in
Comput. Sci., 2976, Springer, Berlin, 2004.
Summary: "We present a probability logic (essentially a first order
language extended with quantifiers that count the fraction of elements
in a model that satisfy a first order formula) that captures uniform
circuit classes such as AC0
and TC0
over arithmetic models, namely,
finite structures with linear order and arithmetic relations. Further
more, the semantics of such a logic with respect to an arithmetic
model can be closely approximated by giving interpretations of for
mulas on finite structures where all relations (including the order) are
restricted to be `modular' (i.e. to act subject to an integer modulus).
In order to give a precise measure of the proximity between satisfac
