Definition:Top (Logic)

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Definition

Top is a constant of propositional logic interpreted to mean the canonical, undoubted tautology whose truth nobody could possibly ever question.

The symbol used is $\top$.


Boolean Interpretation

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

$v \left({\top}\right) = T$

where $T$ symbolises true.


Truth Table

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

$\begin{array}{|c|} \hline \top \\ \hline T \\ \hline \end{array}$


Also denoted as

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


Also see


Technical note

The $\LaTeX$ code for \(\top\) is \top .


Sources