Hi-
It sounds like a checkbox is the incorrect control, perhaps? What about using an Option button? With an Option button, you can give the user 4 options and they choose one.
With a checkbox, each one is independent from the others, each one being true or false.
You could use rules to uncheck other checkboxes if one checkbox is checked. Then you'd also need to add validation. But this sounds like a lot of work.
If you absolutely need four separate true/false checkboxes, let me know. But do try an Option button to see if it addresses your form's need.