Math 2.0

Mathematical logic and foundations Concept

Modus ponens

Builds on Implication

Summary

Modus ponens is the rule of inference that gets qq from the two premises pp and p→qp \to q. pp→qq\frac{p \qquad p \to q}{q} It is valid: when the two premises are true, the conclusion qq is true.

Remarks

Most proof systems for propositional logic use modus ponens as a rule. Its partner modus tollens gets ¬p\neg p from ¬q\neg q and p→qp \to q.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Proposition, concept, no evidence levelPropositionconceptImplication, definition, no evidence levelImplicationdefinitionModus ponens, concept, no evidence levelModus ponensconcept
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  1. Proposition concept
  2. Implication definition
  3. Modus ponens concept

Where this leads

48 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Modus_ponens, lead section
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Aliasesimplication-elimination
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  • edge not_instance_of in: at least one non-example (0 of 1)
  • edge specializes both: the more general notions and the special cases (0 of 1)

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