Modifying Items to Preserve Licensing Local Trees
We are exploring multiple solutions to the problem posed with our first inference rules yesterday. One solution was to change the format of the items to add information about the local trees. A sixth element was added to each item, which indicates the local tree that the item is associated with. * is the default value. R and S represent values assigned to local trees. In our case they range from 0 to 3. R is instantiated from the children of the tree, while S can be directly assigned by label.
Axioms
======
A1: [X, i, *, *, i+1, *] x_i
A2: [X, *, *, *, *, *] X(~, ~, ~)
Inference Rules
========= =====
I1: [Z, i, *, *, n, *][Y, n, j, k, l, *]
------------------------------------ X(~, Z, Y)
[X, i, j, k, l, R]
I2: [Z, i, *, *, j, *][Y, *, *, k, l, *]
------------------------------------ X(~, Z, Y)
[X, i, j, k, l, R]
I3: [Y, i, j, k, m, *][Z, m, *, *, l, *]
------------------------------------ X(~, Y, Z)
[X, i, j, k, l, R]
I4: [Y, i, j, *, *, *][Z, k, *, *, l, *]
------------------------------------ X(~, Y, Z)
[X, i, j, k, l, R]
I5: [Y, i, j, k, l, *]
------------------ X(~, Y, ~)
[X, i, j, k, l, R]
I6: [X, i, n, m, l, R][W, n, j, k, m, S]
------------------------------------ W(X(~, i->n, m->l), n->j, k->m)
[W, i, j, k, l, S]
I7: [X, i, j, *, *, R][W, *, *, k, l, S]
------------------------------------ W(X(~, i->j, ~), ~, k->l)
[W, i, j, k, l, S]
I8: [X, i, j, m, l, R][W, *, *, k, m, S]
------------------------------------ W(X(~, i->j, m->l), ~, k->m)
[W, i, j, k, l, S]
I9: [X, *, *, k, l, R][W, i, j, *, *, S]
------------------------------------ W(X(~, ~, k->l), i->j, ~)
[W, i, j, k, l, S]
I10: [X, i, n, k, l, R][W, n, j, *, *, S]
------------------------------------ W(X(~, i->n, k->l), n->j, ~)
[W, i, j, k, l, S]
I11: [X, *, *, m, l, R][W, i, j, k, m, S]
------------------------------------ W(X(~, ~, m->l), i->j, k->m)
[W, i, j, k, l, S]
I12: [X, i, n, *, *, R][W, n, j, k, l, S]
------------------------------------ W(X(~, n->j, k->l), i->n, ~)
[W, i, j, k, l, S]
I13: [X, i, j, k, l, R][W, *, *, *, *, S]
------------------------------------ W(X(~, n->j, k->l), ~, ~)
[W, i, j, k, l, S]
I14: [X, i, j, k, l, *]
------------------ X
[X, i, j, k, l, R]
Posted by kernco at June 15, 2004 03:02 PM