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You can apparently run a MS SQL server on Linux now, but if you're going to go with a Linux solution, you should use free software where possible. To that end, MySQL is probably your best bet.
As far as language, C++ and Java are good choices (and your framework would be QT for KDE, and GTK+ for gnome), especially if you want to develop a GUI app, and of course you can do Python or Perl.
PHP is a web technology, so you'd have to run a LAMP stack (Linux, Apache, MySQL, PHP).
I'm not sure how the use of AI would play any role in deciding what dev stack to use...
".45 ACP - because shooting twice is just silly" - JSOP, 2010 ----- You can never have too much ammo - unless you're swimming, or on fire. - JSOP, 2010 ----- When you pry the gun from my cold dead hands, be careful - the barrel will be very hot. - JSOP, 2013
That way you can share back-end code with your front-end, and you can even use it to query your database.
Completely cross-platform and all.
Other than that, I've heard Python is pretty cool and good with AI and Big Data, but I haven't used it at all.
And if you're looking to sticking with SQL may I suggest PostgreSQL, which has gained a lot of popularity in the last few years.
Python is the usual goto for AI stuff since it's what a lot of Math guys get taught at Uni so it's what a lot of examples you'll find a written in. Scala or Haskell would probably be good contenders as well if you're preferring a compiled language - you'll not they're all quite trendy at the moment.
As for databases you should check out Neo4J and ArangoDB because I think graph databases are cool - or if you want to stick to a relational DB Postgres is solid.
You should also find some way to use Elasticsearch in your stack because it's what all of the cool kids are doing.
I highly recommend PostgreSQL instead of MySQL. The stored proc code is object oriented. The whole thing is very logical. The only thing good about MySQL is that it is a little more available on web hosting services.
I recommend going toward Node.JS. It's fast and efficient and it's got a lot of good libraries and frameworks to support it. If you are comfortable with NoSQL databases, I'd recommend using MongoDB as your back end database. If you are more of a SQL guy, I'd recommend MySql. As far as AI goes, if you go with Node, you can use Tensor Flow!
Well, it gets funnier. So, I'm on a conf call with IT Support. Seems they can't get Skype for Business to work for me. He fires up team viewer, and the first thing he does? Closes Edge, runs IE11. I wonder what he knows I don't?
<italic>Stuck in a dysfunctional matrix from which I must escape...
"Where liberty dwells, there is my country." B. Franklin, 1783
“They who can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety.” BF, 1759