The edges of the fin isn't black, so it's not fin rot. I would guess the fin was damaged by decore, a filter, or biting. I only see plants in the picture so I don't know what part of your decore you are worried about. You can test ornaments but dragging sheer stockings across it. If the stockings rip, then it was probably the decore. You can take out anything too sharp for stockings and see if the fin damage keeps happening. If the damage does continue, it could be tail biting or filter damage.
It's hard to pin point one exact reason for tail damage unless you see it happen. For all I know he started tail biting because something in his tank upset him. Like, "I hate that cave decore! <bite tail>," or something like that. Since you just noticed the damage, it may take awhile to figure out what really happened to his tail.