The Info List - 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[edit] This can be written as:

( P → Q ) ∧ ( P → ¬ Q ) ↔ ¬ P

displaystyle (Prightarrow Q)land (Prightarrow 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. References[edit]

^ Wansing (Ed.), Heinrich (1996). Negation: A notion in focus. Berlin: Walter de Gruyter. ISBN 3110147696. CS1 maint: Extra text: authors list (link) ^ Haegeman, Lilliane (30 Mar 1995). The Syntax of Negation. Cambridge: Cambridge University Press. p. 70. ISBN 05214