June 15, 2004

Inference rules with all trees 3d

i1.png 

1) [X,i,m,n,l][Y,m,-1,-1,h][Z,h,j,k,n]
   ----------------------------------------
                [W,i,j,k,l]
i2.png 
                         
2) [X,i,m,m+1,i][Y,m,-1,-1,m+1]
   ----------------------------
           [W,i,-1,-1,j]
i3.png 

3) [X,i,j,k,l]
   -----------
   [W,i,j,k,l]

4) [X,i,m,k,l][Y,m,-1,-1,m+1][Z,m+1,j,-1,-1]
   -----------------------------------------
                 [W,i,j,k,l]

5) [X,i,m,n,l][Y,m,-1,-1,m+1][Z,-1,-1,k,n]
   ---------------------------------------
               [W,i,m+1,k,l]

6) [X,-1,-1,m,l][Y,i,-1,-1,i+1][Z,-1,-1,k,m]
   -----------------------------------------
                [W,i,i+1,k,l]


7) [X,-1,-1,n,l][Y,i,-1,-1,i+1][Z,i+1,j,k,l]
   -----------------------------------------
                 [W,i,j,k,l]

8) [X,i,m,-1,-1][Y,m,-1,-1,m+1][Z,m+1,j,k,l]
   -----------------------------------------
                 [W,i,j,k,l]

9) [X,-1,-1,k,l][Y,i,-1,-1,i+1][Z,i+1,j,-1,-1]
   -------------------------------------------
                 [W,i,j,k,l]

10) [X,i,m,-1,-1][Y,m,-1,-1,m+1][Z,-1,-1,k,l]
    -----------------------------------------
                 [W,i,m+1,k,l]

11) [X,-1,-1,-1,-1][Y,i,-1,-1,i+1][Z,i+1,j,k,l]
    -------------------------------------------
                 [W,i,j,k,l]

12) [X,-1,-1,-1,-1][Y,i,-1,-1,i+1][Z,-1,-1,k,l]
    -------------------------------------------
                 [W,i,i+1,k,l]

13) [X,i,m,k,l][Y,m,-1,-1,m+1][Z,-1,-1,-1,-1]
    -----------------------------------------
                [W,i,m+1,k,l]

14) [X,-1,-1,k,l][Y,i,-1,-1,i+1][Z,-1,-1,-1,-1]
    -------------------------------------------
                 [W,i,i+1,k,l]

15) [X,i,m,n,j][Y,m,-1,-1,m+1][Z,m+1,-1,-1,m]
    -----------------------------------------
                 [W,i,-1,-1,j]

16) [X,-1,-1,m,j][Y,j,-1,-1,j+1][Z,i+1,-1,-1,m]
    -------------------------------------------
                 [W,i,-1,-1,j]

17) [X,i,j,-1,-1][Y,j,-1,-1,j+1][Z,j+1,-1,-1,l]
    -------------------------------------------
                  [W,i,-1,-1,l]
Inference rules are based on X and Z subtrees in these forms:
X
xgap.png xrfull.png xlfull.png xup.png xfull.png
zgap.png I1I7I8I11X
zrfull.png I5I6I10I12X
zlfull.png I4I9I4I11X
zup.png I13I14I13I12X
zfull.png I15I16I17I11X
Posted by lemanal at June 15, 2004 04:02 PM
Comments

It should be mentioned that we excluded stating the inverses of rules I4-I17, but they are present. There are also 3 other variations on I2, with X and Y having varying empty sides. This makes a total of 35 rules for this grammar.

Posted by: Colin at June 15, 2004 05:55 PM