Definition:Therefore

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.