| Line 256: |
Line 256: |
| | p | | p |
| | \\ | | \\ |
| − | \overline{~~~~~~~~~~~~} | + | \overline{~~~~~~~~~~~~~~~} |
| | \\ | | \\ |
| | q | | q |
| Line 274: |
Line 274: |
| | p | | p |
| | \\ | | \\ |
| − | =\!=\!=\!=\!=\!=\!= | + | =\!=\!=\!=\!=\!=\!=\!= |
| | \\ | | \\ |
| | p~q | | p~q |
| | + | \end{array}</math> |
| | + | |} |
| | + | |
| | + | <br> |
| | + | |
| | + | {| align="center" cellpadding="8" width="90%" |
| | + | | width="1%" | <big>•</big> |
| | + | | colspan="3" | '''Example 2. Transitivity''' |
| | + | |- |
| | + | | |
| | + | | width="1%" | |
| | + | | colspan="2" | ''Information Reducing Inference'' |
| | + | |- |
| | + | | |
| | + | | |
| | + | | width="1%" | |
| | + | | |
| | + | <math>\begin{array}{l} |
| | + | p \le q |
| | + | \\ |
| | + | q \le r |
| | + | \\ |
| | + | \overline{~~~~~~~~~~~~~~~} |
| | + | \\ |
| | + | p \le r |
| | + | \end{array}</math> |
| | + | |- |
| | + | | |
| | + | | |
| | + | | colspan="2" | ''Information Preserving Inference'' |
| | + | |- |
| | + | | |
| | + | | |
| | + | | |
| | + | | |
| | + | <math>\begin{array}{l} |
| | + | p \le q |
| | + | \\ |
| | + | q \le r |
| | + | \\ |
| | + | =\!=\!=\!=\!=\!=\!=\!= |
| | + | \\ |
| | + | p \le q \le r |
| | \end{array}</math> | | \end{array}</math> |
| | |} | | |} |