Definition:Independent Statements

Definition

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.