Sentence examples for unnecessity from inspiring English sources

${\cal M}, w \models \osim A$ is then defined by requiring that for every $u$$ $wCu \mbox{ implies } {\cal M}, u \not \models A.$ Negation as unnecessity, denoted by $\neg$, is accordingly defined by the following clause: ${\cal M}, w \models \neg A$ iff (there exists $u$ with $wCu \mbox{ and } {\cal M}, u \not \models A)$.

The relational semantics of normal modal logics, however, does come with a commitment to a substantial property of negation understood as impossibility or as unnecessity.

Negation as an "unnecessity" operator $\neg$ in the sense of ("possibly not") is then defined by ${\cal M}, w \models \neg A$ iff $\overline{\llbracket A\rrbracket} \in N w)$, where $\overline{\llbracket A\rrbracket}$ is the complement of $\llbracket A\rrbracket$ with respect to $W$.