Modus Tollens
| Transformation rules |
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| Propositional calculus |
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Rules of inference Rules of replacement Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology |
| Predicate logic |
| Universal generalization Universal instantiation Existential generalization Existential instantiation |
In propositional logic, modus tollens (or modus tollendo tollens and also denying the consequent) (Latin for "the way that denies by denying") is a valid argument form and rule of inference.
It is the inference that
- if implies, and the second premise, is false,
- then it can be logically concluded that must be false.
Modus tollens is closely related to another valid form of argument, modus ponens. There are also similar, but invalid, arguments such as affirming the consequent and denying the antecedent.
The modus tollens rule can be stated formally as:
Where means "P implies Q", means Q is false (not Q). The modus tollens rule, then, is that wherever both "" and "" appear by themselves on a line of a proof, then "" can validly be placed on a subsequent line.
Read more about Modus Tollens: Formal Notation, Explanation, Relation To modus Ponens, Justification Via Truth Table, Formal Proof