Negation introduction

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Negation introduction is a rule of inference, or transformation rule, in the field of propositional calculus.

Negation introduction states that if a given antecedent implies both the consequent and its complement, then the antecedent is a contradiction.[1] [2]

Formal notation

This can be written as: (P \rightarrow Q) \and (P \rightarrow \neg Q) \leftrightarrow \neg P

An example of its use would be an attempt to prove two contradictory statements from a single fact. For example, if a person were to state "When the phone rings I get happy" and then later state "When the phone rings I get annoyed", the logical inference which is made from this contradictory information is that the person is making a false statement about the phone ringing.

External links


  1. Wansing (Ed.), Heinrich (1996). Negation: A notion in focus. Berlin: Walter de Gruyter. ISBN 3110147696.CS1 maint: extra text: authors list (link)<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  2. Haegeman, Lilliane (30 Mar 1995). The Syntax of Negation. Cambridge: Cambridge University Press. p. 70. ISBN 0521464927.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>