Definition:Therefore

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

and denote it:
 * $p \vdash q$

Hence 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 see

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