Modus Tollendo Tollens/Proof Rule/Tableau Form
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Proof Rule
Let $\phi \implies \psi$ be a well-formed formula in a tableau proof whose main connective is the implication operator.
The Modus Tollendo Tollens is invoked for $\phi \implies \psi$ and $\neg \psi$ as follows:
| Pool: | The pooled assumptions of $\phi \implies \psi$ | ||||||||
| The pooled assumptions of $\neg \psi$ | |||||||||
| Formula: | $\neg \phi$ | ||||||||
| Description: | Modus Tollendo Tollens | ||||||||
| Depends on: | The line containing the instance of $\phi \implies \psi$ | ||||||||
| The line containing the instance of $\neg \psi$ | |||||||||
| Abbreviation: | $\text{MTT}$ |
Sources
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $1$: The Propositional Calculus $1$: $2$ Conditionals and Negation