The language where the computer is told what the problem is, not how to solve the problem. So given a database or a set of rules, the computer tries to find a solution matching all the desired properties.
Example 1 (format: input vars => expected output)
Set of rules:
2, 2 => 4; 2, 4 => 6; 4, 4 => 8, etc.
Then program learns that it needs to add all the input variables.
According to Wikipedia, Inductive logic programming (ILP) is a subfield of machine learning which uses logic programming as a uniform representation for examples, background knowledge and hypotheses.
In example, given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples. Inductive logic programming is particularly useful in bioinformatics and natural language processing.
There are some known implementations, such as: