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 $r$.

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 $r$.

Also known as
The symbol $\vdash$ is sometimes called the turnstile symbol (or gate post), and is often (misleadingly) called the assertion sign.

Some older literature uses the symbol $\therefore$ but this is falling out of use. In contrast to $\vdash$, which is a formal symbol used in proof writing, the $\therefore$ symbol is generally used as shorthand for "therefore." So while both symbols are used as abbreviations for the same concept (that is: logical implication), the latter is traditionally classified as a mere punctuation mark, not unlike the ellipsis ($\ldots$).

Also see

 * Definition:Because
 * Definition:Logical Implication
 * Definition:Logical Equivalence
 * Definition:Conditional
 * Definition:Biconditional