nonimplication

The mask is applied using boolean logic known as material nonimplication or abjunction.

Converse Nonimplication in a general Boolean algebra is defined as .

The symbol for material nonimplication is simply a crossed-out material implication symbol.

(Compare material nonimplication in logic.)

Conversely, for the logical connectives , , Material nonimplication, and , the quantifiers flip:

In logic, converse nonimplication is a logical connective which is the negation of the converse of implication.

The universal (and existential) quantifier moves unchanged across the logical connectives , , , and converse nonimplication, as long as the other operand is not affected; that is:

An example for converse nonimplication in computer science can be found when performing a right outer join on a set of tables from a database, if records not matching the join-condition from the "left" table are being excluded.

That is to say that for any two propositions P and Q, the material nonimplication from P to Q is true if and only if P does not imply Q.