  In the present paper we formally define the notion of abstract program
slicing, a general form of program slicing where properties of data are
considered instead of their exact value. This approach is applied to a language
with numeric and reference values, and relies on the notion of abstract
dependencies between program components (statements).
  The different forms of (backward) abstract slicing are added to an existing
formal framework where traditional, non-abstract forms of slicing could be
compared. The extended framework allows us to appreciate that abstract slicing
is a generalization of traditional slicing, since traditional slicing (dealing
with syntactic dependencies) is generalized by (semantic) non-abstract forms of
slicing, which are actually equivalent to an abstract form where the identity
abstraction is performed on data.
  Sound algorithms for computing abstract dependencies and a systematic
characterization of program slices are provided, which rely on the notion of
agreement between program states.
