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The use of Dynamic Epistemic Logic (DEL) in multi-agent planning has led to awidely adopted action formalism that can handle nondeterminism, partialobservability and arbitrary knowledge nesting. As such expressive power comesat 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, ratherthan imposing syntactical constraints, the semantic approach focuses on theaxioms of the logic for epistemic planning. Specifically, we augment the logicof knowledge S5$_n$ and with an interaction axiom called (knowledge)commutativity, which controls the ability of agents to unboundedly reason onthe knowledge of other agents. We then provide a threefold contribution. First,we show that the resulting epistemic planning problem is decidable. In doingso, we prove that our framework admits a finitary non-fixpoint characterizationof common knowledge, which is of independent interest. Second, we studydifferent generalizations of the commutativity axiom, with the goal ofobtaining decidability for more expressive fragments of DEL. Finally, we showthat two well-known epistemic planning systems based on action templates, wheninterpreted under the setting of knowledge, conform to the commutativity axiom,hence proving their decidability.

A Semantic Approach to Decidability in Epistemic Planning (Extended Version)