The Fundamental Rule
Abstract:
Active arcs are called `active' for a very good reason: They "actively" hint at what can be done with them. In particular, we can see at once how to combine them with passive edges to make new edges. The new edges we make may be either passive or active.
Active arcs are called `active' for a very good reason: They "actively" hint at what can be done with them. In particular, we can see at once how to combine them with passive edges to make new edges. The new edges we make may be either passive or active.
The
↗fundamental rule for combining a passive edge and an active edge works as follows: Suppose the active edge goes from node
n1 to node
n2 and has category
C immediately to the right of the dot.
Figure 3: Fundamental Rule Example 1a An example. |
Further, suppose that the passive edge goes from node n2 to node n3 (hence, it starts where the active edge ends) and has category C on its left hand side.
Figure 5: Fundamental Rule Example 1b An example. |
The fundamental rule now allows us to combine these two edges to build a new one that starts in node n1 and ends in n3. For the label of that new edge we move the dot in the active edge one category forward.
Figure 7: Fundamental Rule Example 1c An example. |
Here are two examples to illustrate the fundamental rule.
Figure 9: Fundamental Rule Example 2 Another example. |
Here we have an active edge (the one on the left) which is looking for a np. And immediately to its right we have an np (note that the edge to the right is passive: that is we really know that there is a np between nodes 8 and 10). Using the fundamental rule, we can combine these edges to build a new edge going from node 4 to node 10. Note, that this new edge is active.
Figure 11: Fundamental Rule Example 3 Another example. |
Here we have an active edge (the one on the left) which is looking for a pp. And immediately to the right we have a pp (note that the edge to the right is passive: that is we really know that there is a pp between nodes 8 and 10). Using the fundamental rule, we can combine these edges. Note, that in this case the new edge we have built is passive.