Definition:Because

Definition

If statement $p$ logically implies statement $q$, then we may say:

$q$, because $p$.

The symbol $\dashv$ is interpreted to mean because.

Thus:

$r \dashv p, q$

means:

Given as premises $p$ and $q$, we may validly conclude $r$

or

$r$, because $p$ and $q$.

Also denoted as

Some older literature uses the symbol $\because$ but this is falling out of use.

Also see

• Definition:Therefore
• Definition:Logical Implication
• Definition:Logical Equivalence
• Definition:Conditional
• Definition:Biconditional

Sources

• 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$