Tractability of Theory Patching
  In this paper we consider the problem of `theory patching', in which we are
given a domain theory, some of whose components are indicated to be possibly
flawed, and a set of labeled training examples for the domain concept. The
theory patching problem is to revise only the indicated components of the
theory, such that the resulting theory correctly classifies all the training
examples. Theory patching is thus a type of theory revision in which revisions
are made to individual components of the theory. Our concern in this paper is
to determine for which classes of logical domain theories the theory patching
problem is tractable. We consider both propositional and first-order domain
theories, and show that the theory patching problem is equivalent to that of
determining what information contained in a theory is `stable' regardless of
what revisions might be performed to the theory. We show that determining
stability is tractable if the input theory satisfies two conditions: that
revisions to each theory component have monotonic effects on the classification
of examples, and that theory components act independently in the classification
of examples in the theory. We also show how the concepts introduced can be used
to determine the soundness and completeness of particular theory patching
algorithms.
