As mentioned in Section 2, polarity filtering (Gardent and Kow, 2005) eliminates from the search space those sets of rules which cover the input but cannot possibly lead to a valid derivation either because a substitution node cannot be filled or because a root node fails to have a matching substitution site 4 While (Gardent and Kow, 2005) applies polarity filtering to the initial search space (the set of rules selected by all literals in the input), we apply polarity filtering to each local tree while going up the input tree.
the combinatorics induced by the lack of order in flat semantic representations is less in this task.