Literal (mathematical logic)

In mathematical logic, a literal is an atomic formula (atom) or its negation. The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution.

Literals can be divided into two types:

For a literal ${\displaystyle l}$, the complementary literal is a literal corresponding to the negation of ${\displaystyle l}$, we can write ${\displaystyle {\bar {l}}}$ to denote the complementary literal of ${\displaystyle l}$. More precisely, if ${\displaystyle l\equiv x}$ then ${\displaystyle {\bar {l}}}$ is ${\displaystyle \lnot x}$ and if ${\displaystyle l\equiv \lnot x}$ then ${\displaystyle {\bar {l}}}$ is ${\displaystyle x}$.

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