Definition:Top (Logic)

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 $\top$:

$\map v \top = \T$

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 $T$ or a stylistic variant, and others write it longhand as $\text{true}$.

Also see

• Definition:Tautology

• Definition:Bottom (Logic)
• Definition:Contradiction

Technical note

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

Sources

• 1993: M. Ben-Ari: Mathematical Logic for Computer Science ... (previous) ... (next): Chapter $2$: Propositional Calculus: $\S 2.3$: Boolean interpretations
• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.3.3$