Yes, in the 4th ed grimoire you can put intellego vis into an item to allow it to "learn" skills. 1 Pawn of Int vis gives you 5 points for skills. So 2 pawns would allow an item to learn up to +4 in a skill.
Part of the question is that if the item is "living", could it store its own memories without needing the Int vis?
I don't think that a CrMe effect alone would give it the ability to learn & remember by itself, but if it could I would save about 7 pawns for other effects. - plus saving me finding the Intellego vis
But if I have to I will do it that way - just limits what else the item can do.
Binding a ghost or something similar could work because it was alive at some point and is able to learn things. I don't think I would have to use the Int vis in this case.
Binding a small creature in and then improving its mental facilities would be the same as well I think, the only problem is trying to get rid of the leftover instincts and habits of an animal.
Putting a part of my mind into the item would be nice because it would have my knowledge of Magic Theory. The bad side is that it would be my magic theory, so it would not give a bonus to my lab work.
Can a magic item be taught Magic Theory like other skills? Of course it would be a capped value because as was noted in an earlier thread there is only so much theory you can learn without doing the practical things. But an intelligent item, which can learn (using vis or another method), should be able to learn something - 3? 4? Especially if it was in my lab constantly and watched me doing various things.
The original idea behind the mirror is (sorry for the rough layout)
Living Mirror of assistance (20 pawns)
Talking Mirror with Magic Theory and assorted spells. Mirror is made of polished bronze, 48",30",1", Silver frame 1" by 1.5" - in each corner is a raven looking to the center. Although the mirror is alive, it can only "see" the reflections it contains. All knowledge, spells and effects are used through the image (e.g. Location of people). This is because most imagonem magics do not effect reflections.
When trained the mirror will be able to work as a lab assistant and magical event recorder. This will give a permanent bonus to all lab work. ( 2 int + 4 MT = 6 )
It would have a Rego Terram effect with lots of reqs to move lab equipment about.
It would have an Intellego Imagonem effect to display images which it has reflected.
And a Creo Auram effect to communicate with people, once it has been taught to speak latin.