English Dictionary

material implication

noun

(logic) An implication as defined in classical propositional logic, leading to the truth of paradoxes of material implication such as Q⊢P→Q, to be read as "any proposition whatsoever is a sufficient condition for a true proposition".

The material implication is a logical connective in propositional logic.

意味（1）

(logic) An implication as defined in classical propositional logic, leading to the truth of paradoxes of material implication such as Q⊢P→Q, to be read as "any proposition whatsoever is a sufficient condition for a true proposition".

In the truth table in Figure 1, the first row corresponds to modus ponens, the last row corresponds to modus tollens, the second row could be taken to represent an invalid argument (where P→Q is the argument and P is a premise or conjunction of premises), and the third row helps ensure that an argument of the form P→Q,¬P⊢¬Q is invalid.