I am going to face a following issue:

I'm writing a program that manages some properties, some of them are general and some are specific. Each property is a pair of key and value, and for example: if it is given a general property and other specific property with exactly the same key and value has been existed before then the general property will swap the specific one in the register. If there are two the same general properties - both will remain in the register. And so on; it is like a net of dependencies. In my case I can handle with it intuitively and foresee all cases, but only because the system is not too vast. What if it would?

I have met such problems a few times in many different programs and languages (i.e working with C semaphores) and my question is: How to approach this kind of problem? Is this connected with finite state machine, graph theory or something similar? How to be sure that I have considered the whole system and each possible case? Could you recommend some resources (books, sites) to learn from?