Refinement Operators
A downward (upward) refinement operator is a function
r
: L
H
®
2^L
H
such that for all h'
Îr(
h), h
g
h' (h'
g
h)
Desirable properties:
locally finite
: there exists n such that |
r(
h)| Š n for all h
Î
L
H
complete for L
H
, i.e.all hypos reachable within finite number of steps
L
H
=
r*
(set of starting hypotheses)
proper,
i.e.,there is no h'
Î r(
h) such that h'
º
h.
optimal
, i.e., there is only one path to each h
Î
L
H
.
