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. For example in chess, it should say that the knight can move two squares in front of it by performing two L moves. In checkers it could be that having a piece behind another prevents the other playing from taking that piece.
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).