Let's see how Naturals work for Intervals.
The Natural simply removes any kind of sharp or flat that already applies to the note, such as a sharp or flat in the key signature. When a natural is placed in front of a note, that note will always be one of the white keys on the piano keyboard. Since the natural removes or cancels a sharp or a flat, the natural can raise or lower a note. The natural is the only accidental that can do this.