We propose a novel algorithm for epistemic planning based on dynamic epistemic logic (DEL). The novelty is that we limit the depth of reasoning of the planning agent to an upper bound b, meaning that the planning agent can only reason about higher-order knowledge to at most (modal) depth b. We then compute a plan requiring the lowest reasoning depth by iteratively incrementing the value of b. The algorithm relies at its core on a new type of "canonical" b-bisimulation contraction that guarantees unique minimal models by construction. This yields smaller states wrt. standard bisimulation contractions, and enables to efficiently check for visited states. We show soundness and completeness of our planning algorithm, under suitable bounds on reasoning depth, and that, for a bound b, it runs in (b+1)-EXPTIME. We implement the algorithm in a novel epistemic planner, DAEDALUS, and compare it to the EFP 2.0 planner on several benchmarks from the literature, showing effective performance improvements.

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 S5n 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.

Abstract Designing agents that reason and act upon the world has always been one of the main objectives of the Artificial Intelligence community. While for planning in “simple” domains the agents can solely rely on facts about the world, in several contexts,e.g., economy, security, justice and politics, the mere knowledge of the world could be insufficient to reach a desired goal. In these scenarios,epistemicreasoning,i.e., reasoning about agents’ beliefs about themselves and about other agents’ beliefs, is essential to design winning strategies. This paper addresses the problem of reasoning in multi-agent epistemic settings exploiting declarative programming techniques. In particular, the paper presents an actual implementation of a multi-shotAnswer Set Programming-based planner that can reason in multi-agent epistemic settings, called PLATO (ePistemic muLti-agentAnswer seTprogramming sOlver). The ASP paradigm enables a concise and elegant design of the planner, w.r.t. other imperative implementations, facilitating the development of formal verification of correctness. The paper shows how the planner, exploiting an ad-hoc epistemic state representation and the efficiency of ASP solvers, has competitive performance results on benchmarks collected from the literature.