However, a forest is an implicit collection of many more trees, each of which, when enumerated, has its own probability accumulated from of the parse hyperedges involved.
a forest can be viewed as a virtual weighted k-best list with a huge k. So a rule extracted from a non 1-best parse, i.e., using non 1-best hyperedges, should be penalized accordingly and should have a fractional count instead of a unit one, similar to the E-step in EM algorithms.