Corresponding conditional

In logic, the corresponding conditional of an argument (or derivation) is a material conditional whose antecedent is the conjunction of the argument's (or derivation's) premises and whose consequent is the argument's conclusion. An argument is valid if and only if its corresponding conditional is a logical truth. It follows that an argument is valid if and only if the negation of its corresponding conditional is a contradiction. The construction of a corresponding conditional therefore provides a useful technique for determining the validity of argument.

Consider the argument A:

Either it is hot or it is cold
It is not hot
Therefore it is cold

This argument is of the form:

Either P or Q
Not P
Therefore Q

or (using standard symbols of the propositional calculus):

P ${\displaystyle \lor }$ Q
${\displaystyle \neg }$P
____________
Q

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