From a set of rules, derive the implications? I've only just become interested in this domain, so sorry if I'm not using the correct terminologies.
What I want is the following: Say I have a set of rules (or constraints), I want to derive some implications of those rules.
For example, in Conway's Game of Life, there are 4 basic rules. From these rules, we can see a few patterns emerge. I want a system in which I can input the rules (in some formal language), and it would output at least some of these patterns. Also, if I make a change in any rule, or add a new rule, it should show me the implication of this change (or I should be able to derive it myself from comparing the two outputs).
This should ideally apply to any game that has a set of rules.
Has anything like this ever be made? Is it even feasible? Can you recommend any courses or books where I could start my (re)search? 
All I've found so far are Automated Theorem Provers, but from what I can tell so far, they are way too generic and mathematically oriented (they aim to solve any theory in maths, which has a lot of rules, I just want it for simple games with a small number of rules).
 A: There has been a lot of study dedicated to what you have asked where computer science meets the arts, that subdiscipline is known as "procedural generation."

Two competing methodologies in procedural content generation are teleological and ontogenetic. The teleological approach creates an accurate physical model of the environment and the process that creates the thing generated, and then simply runs the simulation, and the results should emerge as they do in nature.
The ontogenetic approach observes the end results of this process and then attempts to directly reproduce those results by ad hoc algorithms. Ontogenetic approaches are more commonly used in real-time applications such as games. (See "Shattering Reality," Game Developer, August 2006.)

That wiki is rich on information related to the subject. As for books, I have a few on my own to-read list but its a big backlog sadly. I cannot recommend a book I haven't read but there are many books on this subdiscipline that you can find.
