Modus Tollendo Ponens/Proof Rule/Tableau Form
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Proof Rule
Let $\phi \lor \psi$ be a well-formed formula in a tableau proof whose main connective is the disjunction operator.
The Modus Tollendo Ponens is invoked for $\phi \lor \psi$ in either of the two forms:
- Form 1
| Pool: | The pooled assumptions of $\phi \lor \psi$ | ||||||||
| The pooled assumptions of $\neg \phi$ | |||||||||
| Formula: | $\psi$ | ||||||||
| Description: | Modus Tollendo Ponens | ||||||||
| Depends on: | The line containing the instance of $\phi \lor \psi$ | ||||||||
| The line containing the instance of $\neg \phi$ | |||||||||
| Abbreviation: | $\text{MTP}_1$ |
- Form 2
| Pool: | The pooled assumptions of $\phi \lor \psi$ | ||||||||
| The pooled assumptions of $\neg \psi$ | |||||||||
| Formula: | $\phi$ | ||||||||
| Description: | Modus Tollendo Ponens | ||||||||
| Depends on: | The line containing the instance of $\phi \lor \psi$ | ||||||||
| The line containing the instance of $\neg \psi$ | |||||||||
| Abbreviation: | $\text{MTP}_2$ |