Falsum

Definition

Falsum

The falsum, written $\perp$, is the nullary logical constant that is false under every interpretation:

$$v(\perp )=\text{false}\text{for every interpretation }v.$$

It is the canonical contradiction: a formula that needs no atoms yet is never true. The falsum and the verum are each other’s negations:

$$\neg \top \equiv \perp ,\neg \perp \equiv \top .$$

Alternative symbols: $\text{false},\text{F},\text{f},0,\dots$