Negation introduction

Transformation rules
Propositional calculus
Rules of inference
Modus ponens / Modus tollens Biconditional introduction / elimination Conjunction introduction / Simplification Disjunction introduction / elimination Disjunctive / Hypothetical syllogism Constructive / Destructive dilemma Absorption Modus ponendo tollens
Rules of replacement
Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology Negation introduction
Predicate logic
Universal generalization / instantiation Existential generalization / instantiation

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

Category:Propositional Calculus on ProofWiki (GFDLed)

References

↑ Wansing (Ed.), Heinrich (1996). Negation: A notion in focus. Berlin: Walter de Gruyter. ISBN 3110147696.
↑ Haegeman, Lilliane (30 Mar 1995). The Syntax of Negation. Cambridge: Cambridge University Press. p. 70. ISBN 0521464927.