I hope this is what you expect, not quite sure. This is about art in general, not arts.
Mario Bunge's approach (can't remember which book, sorry, he writes about the subject in multiple works, but I believe this is not synthesized as I will present it) is quite interesting. Art is a part of any discipline (a branch of knowledge, as it is studied and transmitted). Arts are not precisely related to aesthetics.
In fact, any discipline has always three possible dimensions: theory, technique, and art.
The theory is all the pure knowledge related to the discipline. If the discipline is "making shoes", the theory is any knowledge that you can, for example, find in books. Which is the best leather. How to create the best protection for the foot, what materials, what practices. If the discipline is "making music", the theory is everything you can learn from books. Harmony, melody, rhythm, etc. It is clear that knowing the theory is not enough to make a useful product. A lot of musicians know a lot of theory, but play horribly. I can probably learn a lot to make a simple shoe on youtube, but that does not guarantee that I can produce a shoe.
Technique is applied knowledge; that is, knowing how to do what we know. The case of music is quite clear: not because I know all notes of a song I will be able to play it. Playing requires exercise, time, memory, the development of physical abilities, etc. The same happens in the case of making shoes.
Art is profitable technique (perhaps this is not the precise term used by Bunge), that is, create a product that others could profit from. One can make an excellent shoe with 30,000 dollars of investment, but that doesn't guarantee other will buy it at such prize. One can create a piece of music by applying all the musical theory rules, but that does not guarantee others will profit from it. But perhaps, having the knowledge and the technique I can create a shoe that will make someone say "Wow! This is a great shoe! I love it!", or "Wow! This is an amazing piece of music! It made me cry!". That is art.
Notice that art is not only related to aesthethics, but mostly to profit in most disciplines. That act of appraising art in this sense is known as art valuation. The expression state of the art clearly summarizes such intention. In certain disciplines, nevertheless, art is strongly linked to aesthetics (thus the profit is mostly emotional). But that doesn't matter, cause all disciplines have different goals. In all cases, the goal is to develop something that others can profit of.