  In this paper we present a counter-example guided abstraction and
approximation refinement (CEGAAR) technique for {\em partial predicate
abstraction}, which combines predicate abstraction and fixpoint approximations
for model checking infinite-state systems. The proposed approach incrementally
considers growing sets of predicates for abstraction refinement. The novelty of
the approach stems from recognizing source of the imprecision: abstraction or
approximation. We use Craig interpolation to deal with imprecision due to
abstraction. In the case of imprecision due to approximation, we delay
application of the approximation. Our experimental results on a variety of
models provide insights into effectiveness of partial predicate abstraction as
well as refinement techniques in this context.
