\begin{definition}[Definition:Independent Statements]
Let $p$ and $q$ be statements.
Let it be the case that:
:$(1): \quad p$ and $q$ are not contrary
:$(2): \quad p$ and $q$ are not subcontrary
:$(3): \quad p$ is not superimplicant to $q$
:$(4): \quad p$ is not subimplicant to $q$
:$(5): \quad p$ and $q$ are not equivalent
:$(6): \quad p$ and $q$ are not contradictory.
Then $p$ and $q$ are '''independent statements'''.
\end{definition}