Implication, in logic, a relationship between two propositions in which the second is a logical consequence of the first. In most systems of formal logic, a broader relationship called material implication is employed, which is read “If A, then B,” and is denoted by A ⊃ B or A → B.

What does material implication mean in logic?

In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or (i.e. either must be true, or.

What is the definition of material implication?

Material implication is meant to capture the truth-functionally minimal sense of any statement of the form “If X then Y”. In this minimal sense, (X→Y) is true whenever X is false, or Y is true, or both.