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 $\top$:
- $\map v \top = \T$
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
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): $\S 2.3.3$