Definition:Because
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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 $q$.
Also denoted as
Some older literature uses the symbol $\because$ but this is falling out of use.
Also see
- Definition:Therefore
- Definition:Logical Implication
- Definition:Logical Equivalence
- Definition:Conditional
- Definition:Biconditional
Sources
- 1980: D.J. O'Connor and Betty Powell: Elementary Logic ... (previous) ... (next): $\S \text{I}: 1$: The Logic of Statements $(1)$