I wouldn't call that kind of logical deductions "intelligence". This is the kind of deductions that a computer can do automatically. Logic is basically only a "calculus" that a calculator can perform much easily than a person.
I think the kind of logical results (or theorems) that are related to intelligence contain something more than syntactic formulas with obvious interpretation

if you understood how artificial intelligence and data mining worked you would not have said what you just said. Find a 10 page essay on data mining, statistical analysis, the job that a statician does and Artificial intelligence and you'll see what i mean by this.

as another forum user on this forum pointed out, our instincts are somewhat based on subconsciess statistics that we pick up over the course of our lives.

Maybe I didn't understand what you meant. For what I know of artificial intelligence, the main point is pattern recognition. But you spoke about "continually adding definitions and logical conclusions to your brain". I don't see how this could be related to artificial intelligence.

If you try to generate all possible definitions and apply to them all possible rules of logic, you obtain an infinite list of theorems, that are for the vast majority of absolute no interest (like the list of all possible results of addition of two integers).

Do you think an artificial intelligence algorithm should be able to find patterns in this infinite list of theorems? Or maybe there should be a way to use artificial intelligence to generate only theorems that have some value?

as time goes on and technology improves, new notions used in these new technologies are produced from combining old notions. Einsteins special and general relativity were impossible with out Newtonian physics for example.

Well, I believe that some form of artificial intelligence capable of recognizing interesting theorems should be possible one day. But the interesting questions are:
- Will this artificial intelligence agree with human judgement on which theorems are to be considered important ?
- Should it be based on the interpretation of logical definitions as structures of the physical world (for example recognizing geometry theorems based on some kind of artificial vision), or can it be done without being aware of the physical world at all ?
( see my other discussion on https://thephilosophyforum.com/discussion/5792/is-mathematics-discovered-or-invented/p1 )

thanks i'll look at it later. I think you would be surprised what modern A.I. is capable of. Do a search on google or bing for what "data mining" is. The amount of things that can be done with data mining is astronomical. Data gathered from data mining is used in artificial intelligence.