Propositional Independence - Formula-Variable Independence and
  Forgetting
  Independence -- the study of what is relevant to a given problem of reasoning
-- has received an increasing attention from the AI community. In this paper,
we consider two basic forms of independence, namely, a syntactic one and a
semantic one. We show features and drawbacks of them. In particular, while the
syntactic form of independence is computationally easy to check, there are
cases in which things that intuitively are not relevant are not recognized as
such. We also consider the problem of forgetting, i.e., distilling from a
knowledge base only the part that is relevant to the set of queries constructed
from a subset of the alphabet. While such process is computationally hard, it
allows for a simplification of subsequent reasoning, and can thus be viewed as
a form of compilation: once the relevant part of a knowledge base has been
extracted, all reasoning tasks to be performed can be simplified.
