Question

What does it mean that new facts can be deduced basing on known facts and rules? An example would be appreciated.

Answer 1

the sentence “new facts can be deduced by known facts and rules” is describing the process of inferring which does exactly that: the knowledge is expanded by adding new facts using the already known facts and rules.

The usual example is this:

known facts:
    All men are mortal
    Socrates is a man

new fact:
    Socrates is mortal.

another example:

1 is a number
if X is a number, succ(X) is a number

from which you can produce infinite new facts:
succ(1) is a number, succ(succ(1)) is a number etc

as hardmath said, “in prolog queries can be ‘answered’ by deduction based on known facts and rules”. it’s worth mentioning that prolog does not try to find all the facts that could be produced by the set of facts and rules; that would be too slow or even impossible.