Line 1,013: |
Line 1,013: |
| A → dA<br> | | A → dA<br> |
| A ← dA<br> | | A ← dA<br> |
| + | A ∨ dA |
| + | |} |
| + | |- |
| + | | f<sub>3</sub> |
| + | | g<sub>15</sub> |
| + | | 1 1 1 1 |
| + | | (( )) |
| + | | True |
| + | | 1 |
| + | |} |
| + | |
| + | <br> |
| + | |
| + | {| align="center" border="1" cellpadding="6" cellspacing="0" style="background:#f8f8ff; font-weight:bold; text-align:center; width:90%" |
| + | |+ '''Table 14. Differential Propositions''' |
| + | |- style="background:#f0f0ff" |
| + | | |
| + | | align="right" | A : |
| + | | 1 1 0 0 |
| + | | |
| + | | |
| + | | |
| + | |- style="background:#f0f0ff" |
| + | | |
| + | | align="right" | dA : |
| + | | 1 0 1 0 |
| + | | |
| + | | |
| + | | |
| + | |- |
| + | | f<sub>0</sub> |
| + | | g<sub>0</sub> |
| + | | 0 0 0 0 |
| + | | ( ) |
| + | | False |
| + | | 0 |
| + | |- |
| + | | |
| + | {| |
| + | | |
| + | <br> |
| + | <br> |
| + | <br> |
| + | |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | g<sub>1</sub><br> |
| + | g<sub>2</sub><br> |
| + | g<sub>4</sub><br> |
| + | g<sub>8</sub> |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | 0 0 0 1<br> |
| + | 0 0 1 0<br> |
| + | 0 1 0 0<br> |
| + | 1 0 0 0 |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | (A)(dA)<br> |
| + | (A) dA <br> |
| + | A (dA)<br> |
| + | A dA |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | Neither A nor dA<br> |
| + | Not A but dA<br> |
| + | A but not dA<br> |
| + | A and dA |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | ¬A ∧ ¬dA<br> |
| + | ¬A ∧ dA<br> |
| + | A ∧ ¬dA<br> |
| + | A ∧ dA |
| + | |} |
| + | |- |
| + | | |
| + | {| |
| + | | |
| + | f<sub>1</sub><br> |
| + | f<sub>2</sub> |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | g<sub>3</sub><br> |
| + | g<sub>12</sub> |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | 0 0 1 1<br> |
| + | 1 1 0 0 |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | (A)<br> |
| + | A |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | Not A<br> |
| + | A |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | ¬A<br> |
| + | A |
| + | |} |
| + | |- |
| + | | |
| + | {| |
| + | | |
| + | <br> |
| + | |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | g<sub>6</sub><br> |
| + | g<sub>9</sub> |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | 0 1 1 0<br> |
| + | 1 0 0 1 |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | (A, dA)<br> |
| + | ((A, dA)) |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | A not equal to dA<br> |
| + | A equal to dA |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | A ≠ dA<br> |
| + | A = dA |
| + | |} |
| + | |- |
| + | | |
| + | {| |
| + | | |
| + | <br> |
| + | |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | g<sub>5</sub><br> |
| + | g<sub>10</sub> |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | 0 1 0 1<br> |
| + | 1 0 1 0 |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | (dA)<br> |
| + | dA |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | Not dA<br> |
| + | dA |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | ¬dA<br> |
| + | dA |
| + | |} |
| + | |- |
| + | | |
| + | {| |
| + | | |
| + | <br> |
| + | <br> |
| + | <br> |
| + | |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | g<sub>7</sub><br> |
| + | g<sub>11</sub><br> |
| + | g<sub>13</sub><br> |
| + | g<sub>14</sub> |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | 0 1 1 1<br> |
| + | 1 0 1 1<br> |
| + | 1 1 0 1<br> |
| + | 1 1 1 0 |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | (A dA)<br> |
| + | (A (dA))<br> |
| + | ((A) dA)<br> |
| + | ((A)(dA)) |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | Not both A and dA<br> |
| + | Not A without dA<br> |
| + | Not dA without A<br> |
| + | A or dA |
| + | |} |
| + | | |
| + | {| |
| + | | |
| + | ¬A ∨ ¬dA<br> |
| + | A ⇒ dA<br> |
| + | A ⇐ dA<br> |
| A ∨ dA | | A ∨ dA |
| |} | | |} |