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Topic: fom - 04 - representation independent semantics
Replies: 0

 fom Posts: 1,037 Registered: 12/4/12
fom - 04 - representation independent semantics
Posted: Dec 7, 2012 3:23 AM

Each of the tables below is the incidence matrix
for an affine geometry with 6 lines.

The tables share the same column names, and, these
names shall be logically prior to the triples
corresponding to the line elements.

Step 1:

Fix a column name

Step 2:

Fix a row name

Step 3.

Construct two truth-table schemata using the triple
from Step 2 with the column from Step 1 in the
rightmost position and separated from the other
two columns from the triple

Step 4.

Interpret the columns of the truth table schemata
by assigning the respective column values from the
incidence matrix from which the row name had been
taken

Step 5.

Evaluate the truth functions described by the
interpreted truth tables

| | | | | | |
| | | | | | | - | - | - |
| - | | | - | | | - | | |
| - | - | | | - | | | | |
| | | - | - | | | | | - |
| | | | | | |
-------------------------------------------------|
| | | | | | |
| | | | | | | | | |
- | - | T | T | T | F | F | F |
- - | | | | | | | |
| - - | | | | | | |
| | | | | | |
-------------------------------------------------|
| | | | | | |
- | - | | | | | | |
| | | | F | T | F | T | F | T |
| - - | | | | | | |
- - | | | | | | | |
| | | | | | |
-------------------------------------------------|
| | | | | | |
- - | | | | | | | |
| - - | F | F | T | F | T | T |
| | | | | | | | | |
- | - | | | | | | |
| | | | | | |
-------------------------------------------------|
| | | | | | |
| - - | | | | | | |
- - | | T | F | F | T | T | F |
- | - | | | | | | |
| | | | | | | | | |
| | | | | | |
-------------------------------------------------|

| | | | | | |
| | | | | | | - | - | - |
| - | | | - | | | - | | |
| - | - | | | - | | | | |
| | | - | - | | | | | - |
| | | | | | |
-------------------------------------------------|
| | | | | | |
- - - | | | | | | |
| - | | F | F | F | T | T | T |
| | - | | | | | | |
- | | | | | | | | |
| | | | | | |
-------------------------------------------------|
| | | | | | |
| - | | | | | | | |
- - - | T | F | T | F | T | F |
- | | | | | | | | |
| | - | | | | | | |
| | | | | | |
-------------------------------------------------|
| | | | | | |
| | - | | | | | | |
- | | | T | T | F | T | F | F |
- - - | | | | | | |
| - | | | | | | | |
| | | | | | |
-------------------------------------------------|
| | | | | | |
- | | | | | | | | |
| | - | F | T | T | F | F | T |
| - | | | | | | | |
- - - | | | | | | |
| | | | | | |
-------------------------------------------------|