Whether or not: the implicature

It may be argued taht the adding of 'or not' to "whether" doesn't add any EXPLICAture to the meaning of what you've explicated. Never mind the implicature.

In most cases, "whether" is used as a pompous synonym of "if" (Grice on 'if').

"We don't know whether the performance is going ahead."

In symbols

~Ka(p)

However, use "whether or not" when there are two alternatives of equal weight.

"Whether or not you decide to come to town with us or stay at home, it won't influence our decision."

And so on.