Jiry, you misunderstand what the Logic is about.
Logic is not something 100% correct. Logic is a process of building conclusion based on highly probable information (facts and relations between these facts).
Under "highly probable" I mean over 90% probability.
Since Logic does not operates 100% correct information, logic generates both correct and incorrect answers. In order to find out if logical conclusion is correct we need to test it. That's why experiment is necessary before we can rely on logic conclusion.
Let's consider an example of logic process:
A) Mary goes to the church.
B) People who go to church believe in God.
C) Mary believes in God
D) People who believe in God believe in life after death.
E) Mary believes in life after death.
Let's try to understand how reliable this logic conclusion could be.
Let assume that every step has 95% probability.
Then total probability would be 0.95 * 0.95 * 0.95 * 0.95 * 0.95 = 0.77 = 77%
1) We may have wrong knowledge that Mary goes to the church (we could confuse Mary with someone else, or Mary might stop going to the church).
2) Not all people who go to church believe in God
3) We could make logical mistake assuming that (A & B) result in C.
4) Not all people who believe in God believe in life after death.
5) We could make logical mistake assuming that (C & D) result in E.
Since logic is not reliable, long logical conclusions are typically could be less probable than even non-reliable observations.
For instance, if Mary’s husband and Mary’s mother mentioned that Mary doesn’t believe in life after death then we’d better rely on their words more than on our 5 step logical conclusion.
Since multi-step logic is unreliable --- multi-step logic is not "the must" component of intelligence. Therefore logic implementation could be skipped in the first strong AI prototypes.
Limited AI can function very well without multi-step logic.