Improve JQL or Issue Navigator to handle Logic

Per multiple internal discussions JQL handles fields as being in three states right now. The 3 statuses are: has value you want, doesn't have the value you want, empty. This causes a break in logic when performing queries such as:

component != ABC

because issues with no component are not returned. Smarter people than me included some formal logic on this:

If we do not want to fix this in the JQL logic due to wanting to stay SQL like, or a high time cost, or too much impact on existing queries, then simply adding some suggestion logic in the Issue Navigator is a pretty acceptable workaround.

For example, search for:

component != ABC

And then have JIRA say:

Did you mean:
component != ABC OR component is EMPTY