Exploration editor suggestion system for generalizing rules

[GoogleCodeExporter]

In as much detail as possible, please describe what you would like to see.

Adding to the TODO list feature request suggested in Issue 859, it would be 
nice to also suggest improvements to the rules. In particular, if a user has a 
state with a NumericInput interaction and has a single answer group with 
several rules:

answer equals 4
answer equals 5
answer equals 6
answer equals 7

There can be three logical conclusions made about the numeric domain, based on 
the inferred intention of the user:

answer is greater than or equal to 4
answer is less than or equal to 7
answer is between 4 and 7, inclusively

All three of these possible suggestions simplify the above 4 rules down to 1, 
which might be what the user originally wants.

Now, this particularly is an issue when training a fuzzy rule. Many examples 
may be provided in the process of training the rule. This suggestion system 
would make an effort to try and find a single explicit rule to add such that:

1. A maximal amount of training data may be removed from the fuzzy rule for 
that group
2. All of the pieces of training data being removed will still be properly 
classified with the new explicit rule

This potentially weakens the general classification, but it strengthens these 
core cases. This suggestions system may also lead to the eventual manual labor 
needed to add answer groups and just infer all of the answers a user wants 
through the process of teaching Oppia possible responses.

Original issue reported on code.google.com by [email protected] on 15 Jul 2015 at 1:19