Definition:Because
From ProofWiki
Definition
If statement $p$ logically implies statement $q$, then we may say:
- $q$, because $p$.
The symbol $\dashv$ is interpreted to mean because.
Thus:
- $r \dashv p, q$
means:
- Given as premises $p$ and $q$, we may validly conclude $r$
or
- $r$, because $p$ and $q$.
Some older literature uses the symbol $\because$ but this is falling out of use.
See Also
Sources
- D.J. O'Connor and Betty Powell: Elementary Logic (1980): $\S 1.1$
