 Sedlár and Punčochář (2019) extend propositional dynamic logic (PDL) into the non-associative Lambek Calculus, which they call Lambek PDL. They give Lambek PDL three informal interpretations, one in terms of actions that modify linguistic resources, another in terms of actions that modify bodies of information, and another in terms of actions that modify the epistemic states of agents (see 2019: 358–539). In their semantics, specific readings of the ternary relation \(R\) from  (13)  above will depend on the interpretation of the information states in their models. In particular, they are interested in threshold cases where commutation, \(x\circ y = y\circ x\), breaks down for channel application. Sedlár (2020) extends the non-associative and non-commutative Lambek calculus with iterative channel operations (both applicational and compositional) under an informational interpretation.