Axioms and Inference Rules for 3-Dimensional Normal Form
Here's Dave's write up of our notes from today. We also converted the grammar Colin posted into normal form, and we are now trying to parse the string from Colin's post using the new axioms, inference rules, and grammar.
Axioms for 3-Dimensional Normal Form
====================================
A1: [X, i, i+1, *, *] X(~, x_i, y)
A2: [X, *, *, i, i+1] X(~, y, x_i-)
A3: [X, i, *, *, i+1] X(~, y, x_i)
A4: [W, i, *, *, i+1] W(x_i(~, ~, ~), ~, ~)
A5: [X, *, *, *, *] X(~, ~, ~)
A6: [X, i, *, *, i+1] x_i
Inference Rules for 3-Dimensional Normal Form
=============================================
I1: [Z, i, *, *, n][Y, n, j, k, l]
------------------------------ X(~, Z, Y)
[X, i, j, k, l]
I2: [Z, i, *, *, n][Y, n, j, k, l]
------------------------------ X(~, Z, Y)
[X, i, j, k, l]
I3: [Y, i, j, k, m][Z, m, *, *, l]
------------------------------ X(~, Y, Z)
[X, i, j, k, l]
I4: [Y, i, j, *, *][Z, k, *, *, l]
------------------------------ X(~, Y, Z)
[X, i, j, k, l]
I5: [Y, i, j, k, l]
--------------- X(~, Y, ~)
[Y, i, j, k, l]
I6: [X, i, n, m, l][W, n, j, k, m]
------------------------------ W(X(~, i->n, m->l), n->j, k->m)
[W, i, j, k, l]
I7: [X, i, j, *, *][W, *, *, k, l]
------------------------------ W(X(~, i->j, ~), ~, k->l)
[W, i, j, k, l]
I8: [X, i, j, m, l][W, *, *, k, m]
------------------------------ W(X(~, i->j, m->l), ~, k->m)
[W, i, j, k, l]
I9: [X, *, *, k, l][W, i, j, *, *]
------------------------------ W(X(~, ~, k->l), i->j, ~)
[W, i, j, k, l]
I10: [X, i, n, k, l][W, n, j, *, *]
------------------------------ W(X(~, i->n, k->l), n->j, ~)
[W, i, j, k, l]
I11: [X, *, *, m, l][W, i, j, k, m]
------------------------------ W(X(~, ~, m->l), i->j, k->m)
[W, i, j, k, l]
I12: [X, i, n, *, *][W, n, j, k, l]
------------------------------ W(X(~, n->j, k->l), i->n, ~)
[W, i, j, k, l]
I13: [X, i, j, k, l][W, *, *, *, *]
------------------------------ W(X(~, n->j, k->l), ~, ~)
[W, i, j, k, l]
Posted by lemanal at June 14, 2004 02:58 PM