Absorption (logic)

Absorption
TypeRule of inference
FieldPropositional calculus
StatementIf implies , then implies and .
Symbolic statement

Absorption is a valid argument form and rule of inference of propositional logic.[1][2] The rule states that if implies , then implies and . The rule makes it possible to introduce conjunctions to proofs. It is called the law of absorption because the term is "absorbed" by the term in the consequent.[3] The rule can be stated:

where the rule is that wherever an instance of "" appears on a line of a proof, "" can be placed on a subsequent line.

  1. ^ Copi, Irving M.; Cohen, Carl (2005). Introduction to Logic. Prentice Hall. p. 362.
  2. ^ "Rules of Inference".
  3. ^ Russell and Whitehead, Principia Mathematica