Let P, Q, R be three statements. Is there a name for the following rule of inference?
If P implies Q, and if P implies R, then P implies both Q and R.
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Sign up to join this communityLet P, Q, R be three statements. Is there a name for the following rule of inference?
If P implies Q, and if P implies R, then P implies both Q and R.
R&W in their landmark work in formal logic : Principia Mathematica, page 110, called it "Principle of Composition" :
if a proposition implies each of two propositions, then it implies their logical product. This is called by Peano the "principle of composition."
The reference is to Giuseppe Peano; see e.g. Logique mathématique (1897).
If P implies Q, and if P implies R, then P implies both Q and R.
The name of the rule is Distribution. See Barker, Stephen (1965), The elements of logic, p. 124-25 (Truth-functional principles for use in deduction).
P -> Q & R
(i.e. how the "and" operator works), or do you mean something more likeP -> Q,R
(i.e. multiple consequents)? – Paul Ross Jul 2 '18 at 7:32