@de budding,
De budding, I think you are making a mistake somewhere. You point out that the BIV has no senses. I disagree. The machine the brain is linked into is taking the place of the senses. Apart from that every human has a "knowapparatus" which are the senses combined with the brain, connected by the nervoussystem. The sum total of this system is what makes us "see" (<--think) what we "see" (<--think). In that sense it does not really matter if I use ultrasonics, infrared or just plain touch; I "see" what my mind tells me I "see".
So what happens is that through our "knowapparatus" we form "thought-objects" ("
judgements"). We do not know that our senses have been replaced by a machine. However, it is a priori true that the thought-objects in the two respective brains (in the vat and in reality) refer to two different things. The thought-objects in the BIV refer to illusions and the thought-objects in the BIR refer to something in reality.
To answer your question:
I do not think a priori logic is really implied in your post de budding. It uses thought objects and a priori intuitions are what form thought objects. Try to realise that the thoughts you have are formed by combining a priori intuitions with a posteriori judgements or perceptions. In that sense logic itself: the existence of the combinations that can be made, is a priori. The moment a judgement is formed it leaves the a priori field so to speak.