A buddy and I are working on a simple 2D top down arena combat game similar to OpenGLAD (grew up on ye olde GLADIATOR).

Thing is, we want to make some substantial deviation from our source of inspiration, including completely destructible/changeable terrain. Like rivers that can be frozen, walls which can be knocked down, etc. As well as letting players and NPC's build new terrain objects, some of which cannot be moved through or seen through.

So I'm tasked with creating the AI, starting with pathfinding.

Because of all the changeable terrain, we need something that can check to see if the player/other NPC's are in line of sight, and which can then check to find current paths around existing terrain, without getting completely confused by new terrain popping up, and old terrain vanishing, and even capable of breaking through terrain.

A lot of that will just be filling in the framework of the feature, but I really just don't know where to start.

What I'm really looking for are relevant websites, books, articles, or keywords to google.

I just can't quite find a direction to start in, because most pathfinding types we've googled up just won't give us even the most basic level of robustness we need.