June 15, 2004

Inference Rules Using New Items

We started to come up with all the possible items for the new set of rules that reference the local trees in the grammar. We ran into more problems at #98. The rules allowing us to let Y be assigned successors when it should be used a node with no current successors in the rule. This causes situations which can't be constructed with the grammar. An example of this will be posted.

Axioms
======
1) [b,5,-1,-1,6,-1]   A1
2) [c,9,-1,-1,10,-1]  A1
3) [a,4,-1,-1,5,-1]   A1
4) [b,6,-1,-1,7,-1]   A1
5) [c,10,-1,-1,11,-1] A1
6) [a,3,-1,-1,4,-1]   A1
7) [b,1,-1,-1,2,-1]   A1
8) [c,12,-1,-1,13,-1] A1
9) [a,0,-1,-1,1,-1]   A1
10) [b,7,-1,-1,8.-1]   A1
11) [c,11,-1,-1,12,-1] A1
12) [a,2,-1,-1,3,-1]   A1
13) [e,8,-1,-1,9,-1]    A1
14) [S,-1,-1,-1,-1,-1] A2
15) [X,-1,-1,-1,-1,-1] A2
16) [Y,-1,-1,-1,-1,-1] A2

Inferred Items
======== =====
17) [S2,5,6,-1,-1,3] (I2,1,14)
18) [S2,6,7,-1,-1,3] (I2,4,14)
19) [S2,1,2,-1,-1,3] (I2,7,14)
20) [S2,7,8,-1,-1,3] (I2,10,14)
21) [S1,-1,-1,9,10,2] (I4,2,16)
22) [S1,-1,-1,10,11,2] (I4,5,16)
23) [S1,-1,-1,11,12,2] (I4,11,16)
24) [S1,-1,-1,12,13,2] (I4,8,16)
25) [S0,4,5,-1,-1,1] (I2,3,15)
26) [S0,3,4,-1,-1,1] (I2,6,15)
27) [S0,0,1,-1,-1,1] (I2,9,15)
28) [S0,2,3,-1,-1,1] (I2,12,15)
29) [S,8,-1,-1,9,0] (I5,13)
30) [Y,5,6,-1,-1,-1] (I7,17,16)
31) [Y,6,7,-1,-1,-1] (I7,18,16)
32) [Y,1,2,-1,-1,-1] (I7,19,16)
33) [Y,7,8,-1,-1,-1] (I7,20,16)
34) [X,-1,-1,9,10,-1] (I9,21,15)
35) [X,-1,-1,10,11,-1] (I9,22,15)
36) [X,-1,-1,11,12,-1] (I9,23,15)
37) [X,-1,-1,12,13,-1] (I9,24,15)
38) [S1,5,6,9,10,2] (I4,30,2)
39) [S1,5,6,10,11,2] (I4,30,5)
40) [S1,5,6,11,12,2] (I4,30,11)
41) [S1,5,6,12,13,2] (I4,30,8)
42) [S1,6,7,9,10,2] (I4,31,2)
43) [S1,6,7,10,11,2] (I4,31,5)
44) [S1,6,7,11,12,2] (I4,31,11)
45) [S1,6,7,12,13,2] (I4,31,8)
46) [S1,1,2,9,10,2] (I4,32,2)
47) [S1,1,2,10,11,2] (I4,32,5)
48) [S1,1,2,11,12,2] (I4,32,11)
49) [S1,1,2,12,13,2] (I4,32,8)
50) [S1,7,8,9,10,2] (I4,33,2)
51) [S1,7,8,10,11,2] (I4,33,5)
52) [S1,7,8,11,12,2] (I4,33,11)
53) [S1,7,8,12,13,2] (I4,33,8)
54) [S0,4,5,9,10,1] (I2,3,34)
55) [S0,4,5,10,11,1] (I2,3,35)
56) [S0,4,5,11,12,1] (I2,3,36)
57) [S0,4,5,12,13,1] (I2,3,37)
58) [S0,3,4,9,10,1] (I2,6,34)
59) [S0,3,4,10,11,1] (I2,6,35)
60) [S0,3,4,11,12,1] (I2,6,36)
61) [S0,3,4,12,13,1] (I2,6,37)
62) [S0,0,1,9,10,1] (I2,3,34)
63) [S0,0,1,10,11,1] (I2,9,35)
64) [S0,0,1,11,12,1] (I2,9,36)
65) [S0,0,1,12,13,1] (I2,9,37)
66) [S0,2,3,9,10,1] (I2,12,34)
67) [S0,2,3,10,11,1] (I2,12,35)
68) [S0,2,3,11,12,1] (I2,12,36)
69) [S0,2,3,12,13,1] (I2,12,37)
70) [X,5,6,9,10,2] (I13,15,38)
71) [X,5,6,10,11,2] (I13,15,39)
72) [X,5,6,11,12,2] (I13,15,40)
73) [X,5,6,12,13,2] (I13,15,41)
74) [X,6,7,9,10,2] (I13,15,42)
75) [X,6,7,10,11,2] (I13,15,43)
76) [X,6,7,11,12,2] (I13,15,44)
77) [X,6,7,12,13,2] (I13,15,45)
78) [X,1,2,9,10,2] (I13,15,46
79) [X,1,2,10,11,2] (I13,15,47
80) [X,1,2,11,12,2] (I13,15,48)
81) [X,1,2,12,13,2] (I13,15,49)
82) [X,7,8,9,10,2] (I13,15,50)
83) [X,7,8,10,11,2] (I13,15,51)
84) [X,7,8,11,12,2] (I13,15,52)
85) [X,7,8,12,13,2] (I13,15,53)
86) [S0,4,6,9,10,-1] (I1,70,3)
87) [S0,4,6,10,11,-1] (I1,71,3)
88) [S0,4,6,11,12,-1] (I1,72,3)
89) [S0,4,6,12,13,-1] (I1,73,3)
90) [S0,0,2,9,10,-1] (I1,78,9)
91) [S0,0,2,10,11,-1] (I1,79,9)
92) [S0,0,2,11,12,-1] (I1,80,9)
93) [S0,0,2,12,13,-1] (I1,81,9)
94) [S2,4,7,9,10,3] (I10,18,86)
95) [S2,4,7,10,11,3] (I10,18,87)
96) [S2,4,7,11,12,3] (I10,18,88)
97) [S2,4,7,12,13,3] (I10,18,89)
98) [Y,4,8,12,13,3] (I10,20,97)
Posted by kernco at June 15, 2004 05:38 PM