  The limit behavior of inductive logic programs has not been explored, but
when considering incremental or online inductive learning algorithms which
usually run ongoingly, such behavior of the programs should be taken into
account. An example is given to show that some inductive learning algorithm may
not be correct in the long run if the limit behavior is not considered. An
inductive logic program is convergent if given an increasing sequence of
example sets, the program produces a corresponding sequence of the Horn logic
programs which has the set-theoretic limit, and is limit-correct if the limit
of the produced sequence of the Horn logic programs is correct with respect to
the limit of the sequence of the example sets. It is shown that the GOLEM
system is not limit-correct. Finally, a limit-correct inductive logic system,
called the prioritized GOLEM system, is proposed as a solution.
