Definition:Bottom (Logic)

Definition

Bottom is a constant of propositional logic interpreted to mean the canonical, undoubted contradiction whose falsehood nobody could possibly ever question.

The symbol used is $\bot$.

Boolean Interpretation

There is only one boolean interpretation for $\bot$:

$v \left({\bot}\right) = F$

where $F$ symbolises false.

Truth Table

The characteristic truth table of the bottom constant $\bot$ of propositional logic is as follows:

$\begin{array}{|c|} \hline \bot \\ \hline F \\ \hline \end{array}$

Also denoted as

Not all sources use the $\bot$ symbol. Some use $\text F$ or a stylistic variant, and others write it longhand as $\text{false}$.

Technical note

The $\LaTeX$ code for $\bot$ is \bot .