Matrix is a communications network.
It has a client-server, server-server decentralized architecture.
Rooms are synced (eventually consistent) among all servers with clients participating in the room.

Matrix supports "Application Services", which are limited to funcion in a passive mode, meaning they only piggyback on top of the existing protocols.

Synapse, a Matrix server implementation, supports "Modules"

The Matrix devs recognize the need for a robust reputation system and are in pursuit of funding and development for that purpose.