\begin{definition}[Definition:Set of Literals]
Let $S$ be a set.
A '''set of literals''' on $S$ is a triple $\struct {S^\pm, \iota, \theta}$ where:
:$S^\pm$ is a set
:$\iota : S \to S^\pm$ is a mapping, the '''canonical injection'''
:$\theta : S^\pm \to S^\pm$ is an involution without fixed points, the '''inversion mapping''', and we also denote $\map \theta s = s^{-1}$
such that $S^\pm = \iota \sqbrk S \sqcup \theta \sqbrk {\iota \sqbrk S}$ is the disjoint union of the image of $S$ under $\iota$ and its image under $\theta$.
Explicitly, $S^\pm$ can be defined as follows.
Let $S^\pm = S \sqcup S = S \times \set 0 \cup S \times \set 1$ be the disjoint union of $S$ with $S$.
Let $\iota: S \to S^\pm$ be the canonical mapping:
:$s \mapsto \tuple {s, 0}$
Let $\theta : S^\pm \to S^\pm$ be the mapping:
:$\tuple {s, i} \mapsto \tuple {s, 1 - i}$
{{tidy|The above phrasing is not up to par}}
\end{definition}