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 $$r$$," or "$$p$$ and $$q$$, therefore $$r$$."

Thus 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.