A problem was pointed out by Ian with the factored 3d rules of yesterday. The 3rd rule in the first case did not account for W already having a second dimensional yield. The first attempt to fix this problem was to separate the construction of W into three steps: constructing W1 from the third dimensional yield, constructing W2 from the second dimensional yield, and constructing W by combining W1 and W2 into the final W. The problem, of course, is that the labels used are not restricted, i.e. W2 could be constructed and then used as X in some other rule. The solution to this would be to introduce another element in the item to keep track of such information. This solution is the flagged version of items that we have already come up with and are justifiying. Therefore, the factorization of the 3d rules took us back to the flagged set of rules we were working with.
Axioms
A1: [x, i, ~, ~, i+1]
A2: [X, ~, ~, ~, ~]
Inference Rules
[X,a,b,c,d] W
I1: ----------- \
[W,a,b,c,d] X
X
[X,b,c,d,e] [Y,a,b,e,f] /|
I2: ------------------------- W |
[W,first,last,First,Last] \|
Y
[Y,a,b,c,d] [Z,d,~,~,e] X
I3: ----------------------- W / \
[X,a,b,first,last] Y Z
[Y,a,~,~,b] [Z,b,c,d,e] X
I4: ----------------------- W / \
[X,first,last,d,e] Y Z
[X,b,c,d,e] [W,a,b,e,f]
I5: -------------------------- X
[W1,first,last,First,Last] \
W
[Y,a,b,c,d] [Z,d,~,~,e] W2
I6: ------------------------ / \
[W2,a,b,first,last] Y Z
[Y,a,~,~,b] [Z,b,c,d,e] W2
I7: ----------------------- / \
[W2,first,last,d,e] Y Z
[W1,a,b,e,f] [W2,b,c,d,e] W--W1
I8: ------------------------- |
[W,first,last,First,Last] W2
Posted by kernco at June 18, 2004 03:01 PM