The use of Dynamic Epistemic Logic (DEL) in multi-agent planning has led to a widely adopted action formalism that can handle nondeterminism, partial observability and arbitrary knowledge nesting. As such expressive power comes at the cost of undecidability, several decidable fragments have been isolated, mainly based on syntactic restrictions of the action formalism. In this paper, we pursue a novel semantic approach to achieve decidability. Namely, rather than imposing syntactical constraints, the semantic approach focuses on the axioms of the logic for epistemic planning. Specifically, we augment the logic of knowledge S5$_n$ and with an interaction axiom called (knowledge) commutativity, which controls the ability of agents to unboundedly reason on the knowledge of other agents. We then provide a threefold contribution. First, we show that the resulting epistemic planning problem is decidable. In doing so, we prove that our framework admits a finitary non-fixpoint characterization of common knowledge, which is of independent interest. Second, we study different generalizations of the commutativity axiom, with the goal of obtaining decidability for more expressive fragments of DEL. Finally, we show that two well-known epistemic planning systems based on action templates, when interpreted under the setting of knowledge, conform to the commutativity axiom, hence proving their decidability.

Epistemic planning is a very expressive framework that extends automated planning by the incorporation of dynamic epistemic logic (DEL). We provide complexity results on the plan existence problem for multi-agent planning tasks, focusing on purely epistemic actions with propositional preconditions. We show that moving from epistemic preconditions to propositional preconditions makes it decidable, more precisely in EXPSPACE. The plan existence problem is PSPACE-complete when the underlying graphs are trees and NP-complete when they are chains (including singletons). We also show PSPACE-hardness of the plan verification problem, which strengthens previous results on the complexity of DEL model checking.

From a theoretical perspective, judging the expressivity of planning formalisms helps to understand the relationship of different representations and to infer theoretical properties. From a practical point of view, it is important to be able to choose the best formalism for a problem at hand, or to ponder the consequences of introducing new representation features. Most work on the expressivity is based either on compilation approaches, or on the computational complexity of the plan existence problem. Recently, we introduced a new notion of expressivity. It is based on comparing the structural complexity of the set of solutions to a planning problem by interpreting the set as a formal language and classifying it with respect to the Chomsky hierarchy. This is a more direct measure than the plan existence problem and enables also the comparison of formalisms that can not be compiled into each other. While existing work on that last approach focused on different hierarchical problem classes, this paper investigates STRIPS with and without conditional effects; though we also tighten some existing results on hierarchical formalisms. Our second contribution is a discussion on the language-based expressivity measure with respect to the other approaches.

Where information grows abundant, attention becomes a scarce resource. As a result, agents must plan wisely how to allocate their attention in order to achieve epistemic efficiency. Here, we present a framework for multi-agent epistemic planning with attention, based on Dynamic Epistemic Logic (DEL, a powerful formalism for epistemic planning). We identify the framework as a fragment of standard DEL, and consider its plan existence problem. While in the general case undecidable, we show that when attention is required for learning, all instances of the problem are decidable.

Epistemic planning is a very expressive framework that extends automated planning by the incorporation of dynamic epistemic logic (DEL). We provide complexity results on the plan existence problem for multi-agent planning tasks, focusing on purely epistemic actions with propositional preconditions. We show that moving from epistemic preconditions to propositional preconditions makes it decidable, more precisely in EXPSPACE. The plan existence problem is PSPACE-complete when the underlying graphs are trees and NP-complete when they are chains (including singletons). We also show PSPACE-hardness of the plan verification problem, which strengthens previous results on the complexity of DEL model checking.

The field of deterministic AI planning can roughly be divided into two approaches - classical state-based planning and hierarchical task network (HTN) planning. The plan existence problem of the former is known to be decidable while it has been proved undecidable for the latter. When extending HTN planning by allowing the unrestricted insertion of tasks and ordering constraints, one obtains a form of planning which is often referred to as "hybrid planning." We present a simplified formalization of HTN planning with and without task insertion. We show that the plan existence problem is undecidable for the HTN setting without task insertion and that it becomes decidable when allowing task insertion. In the course of the proof, we obtain an upper complexity bound of EXPSPACE for the plan existence problem for propositional HTN planning with task insertion.