Well, i still think "the AI is cheating" is a good way of describing what's going on without too long descriptions. I could, but I will not go into a long discussion about defining AI and programming.
To the point:
The game is multiplayer and there are 6 AI and 2 Players.
There are 4 permanent alliances with the players in the same alliance.
We have no open borders with anyone or never had in the entire game actually.
And there where no wars during these trespassing occations.
My computer is the server in LAN, so it's not lag. The other player also saw the same thing, has a totally different computer, so it would be strange if both had the same graphical bug.
On the first occasion the AI went in with a Galley(Settler, Archer),
It moved in one square one turn. Next turn is stood still, then moved another square further into my territory.
There it remained a few turns until it sailed away.
The second occation several Detroyers entered my territory(2-3 squares in)
in several places. Not sure if they entered at the same time.
They could have been there for a few turns before I noticed it.
A few turns they stayed inside, then they declared war.
The destroyers were still inside my territory, and moved far inside and started pillaging my fishing boates. I know they started inside my territory because of the number of squares they had to move to get to where they pillaged.
(I had several islands with water between them that were completely within my borders)
Maybe this description helps. Graphical bug or programming bug... Not knowing where units really are or not knowing what rules they follow is equally silly in a strategic game. Cheating or not
It could be that the AI pathfinding has a bug that causes them to be able to enter culture borders sometimes. Since then they have a hard time moving around ones inside, it is probably something with the border edges.