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

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.

DELPHIC: Practical DEL Planning via Possibilities (Extended Version)

Dynamic Epistemic Logic (DEL) provides a framework for epistemic planning that is capable of representing non-deterministic actions, partial observability, higher-order knowledge and both factual and epistemic change. The high expressivity of DEL challenges existing epistemic planners, which typically can handle only restricted fragments of the whole framework. The goal of this work is to push the envelop of practical DEL planning, ultimately aiming for epistemic planners to be able to deal with the full range of features offered by DEL. Towards this goal, we question the traditional semantics of DEL, defined in terms on Kripke models. In particular, we propose an equivalent semantics defined using, as main building block, so-called possibilities: non well-founded objects representing both factual properties of the world, and what agents consider to be possible. We call the resulting framework DELPHIC. We argue that DELPHIC indeed provides a more compact representation of epistemic states. To substantiate this claim, we implement both approaches in ASP and we set up an experimental evaluation to compare DELPHIC with the traditional, Kripke-based approach. The evaluation confirms that DELPHIC outperforms the traditional approach in space and time.

Modelling Multi-Agent Epistemic Planning in ASP

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, epistemic reasoning, 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-shot Answer Set Programming-based planner that can reason in multi-agent epistemic settings, called PLATO (ePistemic muLti-agent Answer seT programming 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. It is under consideration for acceptance in TPLP.