Summary: Results from MathSciNet: Mathematical Reviews on the Web
c Copyright American Mathematical Society 2006
MR2095228 (2005f:68050) 68Q19 03B48 03C13 68Q15
Arratia, Argimiro (YV-SBOL); 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
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-