Implication without if statement In logic, can we have an implication if there is no "if"?
Ex, John shall do $x$ regardless
Then is this an implication?
 A: It could be, if you want it to. You can always make it an if sentence. Like "If $1+1=2$, then John shal do $x$." But as it stands in your question, no, it's not an implication.
A: Given what you posted given the proposition $J:=$"John shall do x regardless", in logic, is simply $J$, assuming $J:=$ "John shall do x."
Suppose we fill out the statement, e.g. John shall do x regardless of P or Q.
Then we would have $(P\lor Q) \to J$ which is true regardless of whether $P \lor Q$ is true.
A: The word "regardless" in your example doesn't modify the meaning of the sentence. Its job is merely to explicitly point out that there is no implication or condition present.
It is up to the reader/listener to figure out from context which potential implication it is he should note isn't there.
In mathematics, where our ideal is that all conditions are stated explicitly, we have no need for representing such things in symbolic logic. Then, conditions are never just assumed to be there if they're not actually written down, so a symbolic form of "observe that there is no condition here" is not necessary. Of course, we can still ask the reader to think about a particular property of a formula, but we use words for that, not symbols.
