Compositionality is handled by linking or coindexing the arguments of the conjoined HMMs.
a sentence like The person to the left of the backpack approached the trashcan would be represented as a conjunction of person(p 0 ), to-the-left-of(p 0 , p 1 ), backback(p 1 ), approached(p 0 , p 2 ), and trash-can(p 2 ) over the three participants p 0 , p 1 , and p 2 .