Definition:Therefore

Definition
If statement $p$ logically implies statement $q$, then we may say:
 * $p$, therefore $q$.

The symbology:
 * $p, q \vdash r$

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

So the symbol $\vdash$ is interpreted to mean therefore.

Thus, $p, q \vdash r$ reads as:
 * $p$ and $q$, therefore $r$.

The symbol $\vdash$ is sometimes called the turnstile symbol, and is often (misleadingly) called the assertion sign.

A fallacy may be indicated by $p, q \not \vdash r$, which can be interpreted as:
 * Given as premises $p$ and $q$, we may not validly conclude $r$.

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

Also see

 * Because
 * Interderivable (Logical Equivalence)
 * Conditional
 * Material Equivalence