Assuming you have three checkboxes to test your code might work along these lines
Code:
Sub SetCheck()
Dim bChecked As Boolean
bChecked = False
With ActiveDocument
If .FormFields("Check1").CheckBox.Value Then bChecked = True
If .FormFields("Check2").CheckBox.Value Then bChecked = True
If .FormFields("Check3").CheckBox.Value Then bChecked = True
.FormFields("Check4").CheckBox.Value = bChecked
End With
End Sub
Assign the macro to run on exit for each of the formfields that trigger the summary checkbox.