In propositional logic, the operator $\rightarrow$ denotes implication, so $$ A \rightarrow B $$ means: If A is true, it follows that B is also true.
Question: Is there a symbol $???$ to denote the independence of two statments? $$ A\space ???\space B $$ meaning that neither does A imply B nor vice versa. I guess, this could be written as $$ \neg(A \rightarrow B)\space \land\space\neg(B \rightarrow A) $$ but I am looking for a more concise notation.
If logical independence is meant -- which presumably it is -- then we normally say that $B$ is logically independent of a given $A$ if neither $B$ nor $\neg B$ logically follows from $A$.
So two-way logical independence comes to this: $A \nvdash B$ and $B \nvdash A$ and $A \nvdash \neg B$ and $B \nvdash \neg A$ too. Or equivalently $\nvdash A \to B$ and $\nvdash B \to A$ and $\nvdash A \to \neg B$ and $\nvdash B \to \neg A$.
Or you might want to do all this with a semantic rather than a syntactic turnstile. But either way, you need more than bare material conditionals, then, to regiment a claim of logical independence.