Compositionality
Compositionality concerns composing systems from subsystems. Issues of compositionality had proven to be serious limitations for previous theories of computation including the lambda calculus and Petri nets. E.g., two lambda expressions are not a lambda expression and two Petri nets are not a Petri net and cannot influence each other.
In his doctoral dissertation Gul Agha addressed issues of compositionality in the Actor model. Actor configurations have receptionists that can receive messages from outside and may have the addresses of the receptionists of other Actor configurations. In this way two Actor configurations can be composed into another configuration whose subconfigurations can communicate with each other. Actor configurations have the advantage that they can have multiple Actors (i.e. the receptionists) which receive messages from outside without the disadvantage of having to poll to get messages from multiple sources (see issues with getting messages from multiple channels).
Read more about this topic: Actor Model Later History