Multi-agent Epistemic Planning

• Multi-agent epistemic planning (MEP) is an automated planning approach where agents reason about both the state of the world and each other’s beliefs.
• It integrates techniques from dynamic logic, ASP, and perspective-based reasoning to manage epistemic states and handle nested beliefs.
• MEP methods facilitate coordination and communication in complex environments by modeling actions, observability, and information flow among agents.

Multi-agent epistemic planning (MEP) is an automated planning setting in which multiple agents reason not only about the state of the world but also about information flow, including what agents know or believe about the world and about one another’s knowledge or beliefs. In recent years, MEP has received attention from both dynamic logic and planning communities, and its current formulations range from Dynamic Epistemic Logic (DEL)-style Kripke-state planning to compilation-based, Answer Set Programming (ASP)-based, and perspective-based approaches. A representative generalization is the planner MEPK, whose representation language allows the initial KB and the goal, and the preconditions and effects of actions, to be arbitrary multi-agent epistemic formulas, with solutions represented as action trees branching on sensing results (Huang et al., 2018).

1. Formal setting and semantic models

A standard formalization begins with a finite set of agents and a finite set of propositional fluents. In one formulation, the epistemic language includes fluent formulas together with modal operators for individual belief, group knowledge, and common knowledge, for example $B_{ag_i}\phi$, $E_\alpha \phi$, and $C_\alpha \phi$; in another, formulas are generated from propositional combinations, individual belief $i\,\phi$, group belief $[\alpha]\phi$, and common belief $C^\alpha \phi$ (Fabiano, 2019, Burigana et al., 2020).

The dominant model-theoretic semantics uses pointed Kripke structures. A Kripke structure $M=(S,\pi,R_1,\ldots,R_n)$ has a nonempty set of worlds, a valuation over fluents, and one accessibility relation per agent. Satisfaction is standard for propositional formulas; $(M,s)\models B_{ag_i}\phi$ iff $\phi$ holds at every $t$ such that $E_\alpha \phi$0; and $E_\alpha \phi$1 iff $E_\alpha \phi$2 holds in all worlds reachable from $E_\alpha \phi$3 by any finite chain of relations $E_\alpha \phi$4 for agents in $E_\alpha \phi$5. The axiomatic regime distinguishes knowledge and belief: for S5, each $E_\alpha \phi$6 is reflexive, transitive, and euclidean, whereas for KD45 each $E_\alpha \phi$7 is serial, transitive, and euclidean (Fabiano, 2019).

MEP has also been defined through alternative epistemic-state representations. In the “possibilities” semantics used by PLATO, a possibility assigns truth values to fluents and, for each agent, an information state that is itself a set of possibilities; entailment is defined inductively, and common belief is characterized by iterated group belief $E_\alpha \phi$8 for every $E_\alpha \phi$9 (Burigana et al., 2020). Perspective-based lines of work replace explicit Kripke models with observation functions and justified perspectives: in the JP and PJP traditions, an agent’s belief is evaluated on a local history reconstructed from what the agent has observed, while GJP extends that idea to group belief operators such as uniform belief, distributed belief, and common belief (Li et al., 2024, Hu et al., 2024).

At the planning level, a common abstraction is a domain tuple with fluents, agents, actions, an initial epistemic condition, and a goal formula. One explicit definition is $C_\alpha \phi$0, where $C_\alpha \phi$1 is a set of parametrized actions, $C_\alpha \phi$2 is an initial belief formula, and $C_\alpha \phi$3 is a goal formula (Burigana et al., 2020).

2. Actions, observability, and epistemic state change

The standard action formalism in MEP is DEL event models. An action model is typically written as $C_\alpha \phi$4, where $C_\alpha \phi$5 is a finite set of events, $C_\alpha \phi$6 captures each agent’s uncertainty over events, $C_\alpha \phi$7 assigns an epistemic precondition to each event, and $C_\alpha \phi$8 specifies ontic effects. Executing $C_\alpha \phi$9 in a pointed model $i\,\phi$0 yields a product update whose worlds are the pairs $i\,\phi$1 satisfying the event precondition, whose accessibility relations combine world-level and event-level uncertainty, and whose valuation reflects event postconditions (Alshehri et al., 2019). A closely related presentation appears in generalized DEL planning tasks, where event models may also have designated events and post-functions over propositions (Burigana et al., 2023).

Action vocabularies are usually divided into ontic actions, sensing actions, and announcement actions. In the language $i\,\phi$2, ontic actions change fluents, sensing actions let an agent learn the value of a fluent, and announcement actions change beliefs through public or private announcements. Observability is classified per agent as fully, partial, or oblivious, and the language includes statements such as executable, causes, determines, announces, observes, and aware_of (Burigana et al., 2020). Public announcement, private announcement, and lying or deceptive announcements are all expressible as event models with different event structures and indistinguishability relations (Fabiano, 2021).

The general planner MEPK extends this design space in several specific ways. Existing implementations of multi-agent epistemic planning were described as being based on compilation into classical planning and as suffering from limitations such as generating only linear plans, restriction to public actions, and incapability to handle disjunctive beliefs. MEPK instead uses a representation language in which the initial KB and the goal, and the preconditions and effects of actions, can be arbitrary multi-agent epistemic formulas, and the solution is an action tree branching on sensing results. To support efficient reasoning in the multi-agent KD45 logic, it uses a normal form called alternating cover disjunctive formulas (ACDFs), together with basic revision and update algorithms for ACDFs. It also handles static propositional common knowledge, called constraints, and adapts the PrAO algorithm for contingent planning (Huang et al., 2018).

A separate DEL-based tradition emphasizes perspective shifts rather than only product updates. In that framework, the local state $i\,\phi$3 associated with an agent $i\,\phi$4 is the set of worlds that $i\,\phi$5 considers possible, and the key property is $i\,\phi$6 iff $i\,\phi$7. This enables planning notions in which one agent reasons about what another agent can see or do after observing prior actions, which is central to implicit coordination (Engesser et al., 2017).

3. Planner architectures and representation strategies

One major family of planners compiles bounded-depth epistemic reasoning into classical planning. In the communication-planning work built on the planner of Muise et al. (2015), MEP problems with bounded modal depth are compiled into classical planning by encoding each belief atom $i\,\phi$8 up to depth $i\,\phi$9 as a fresh fluent; communication and domain actions are then interleaved in a sequential plan, and the implementation relies on off-the-shelf classical planners rather than epistemic-specific heuristics (Alshehri et al., 2019). RP-MEP develops this direction for nested belief by compiling restricted modal literals into propositional fluents and translating epistemic actions into classical or FOND operators with conditional effects; the compilation is exponential in the nesting bound $[\alpha]\phi$0, but once compiled, synthesis is delegated to classical planning technology (Muise et al., 2021).

A second family keeps the epistemic semantics explicit but changes the implementation substrate. PLATO is a multi-shot ASP-based planner whose state encoding includes atoms such as possible_world, holds, believes, and pointed; it is organized into #program base, #program step(t), and #program check(t) together with a Python control script over the clingo API. Three formal propositions establish entailment correctness, initial-state correctness, and action correctness relative to the underlying semantics, and the implementation exploits multi-shot solving so that learned nogoods are reused across planning depths (Burigana et al., 2020).

A third family decomposes planning and epistemic reasoning. In the Functional STRIPS approach, epistemic formulas are evaluated lazily by external black-box functions rather than by explicit Kripke-model compilation. The crucial modeling abstraction is the perspective function $[\alpha]\phi$1, representing what agent $[\alpha]\phi$2 sees in a state; knowledge is defined through the relation between seeing and truth, and group operators are implemented through unions and fixed-point constructions over such perspectives. This avoids the exponential pre-compilation step and supports continuous and numerical features without propositionalization (Hu et al., 2019).

Modular systems have also been designed to separate parsing, update, search, and output. One C++ solver design starts from EFP, re-implements a planner supporting the full $[\alpha]\phi$3 language over $[\alpha]\phi$4 or $[\alpha]\phi$5, and structures it into an input parser, state updater, forward-search module, plan extractor, and output formatter. It employs dynamic programming via memoization of visited epistemic states up to isomorphism, prunes unreachable worlds on the fly, and is designed to support parametric state representations such as standard Kripke structures and Gerbrandy-style “possibility sets” (Fabiano, 2019).

These architectural differences correspond to different trade-offs. Compilation-based systems reduce online reasoning to classical search; native symbolic and ASP-based systems preserve richer update semantics inside the planner; and decomposed approaches shift epistemic inference to external procedures. This suggests that MEP is best viewed not as a single algorithmic paradigm but as a family of solver designs organized around distinct choices of state representation, update mechanism, and search control.

4. Complexity, tractable fragments, and decidability

The computational difficulty of MEP is well documented. For satisfiability, the reviewed results state that SAT in $[\alpha]\phi$6 or $[\alpha]\phi$7 is NP-complete; in $[\alpha]\phi$8 and $[\alpha]\phi$9 for $C^\alpha \phi$0 it is PSPACE-complete; and in common-knowledge logics $C^\alpha \phi$1 and $C^\alpha \phi$2 for $C^\alpha \phi$3 it is EXPTIME-complete. For plan existence in DEL, the cited complexity profile is: non-factual actions with propositional preconditions yield EXPSPACE, factual actions with propositional preconditions are non-elementary, and factual actions with epistemic preconditions are undecidable (Fabiano, 2019).

A substantial line of work therefore isolates tractable fragments. Knowledge compilation for multi-agent epistemic logic introduces the separability-based disjunctive normal form SDNF for $C^\alpha \phi$4, proves that every epistemic formula can be equivalently compiled into SDNF, and shows that major reasoning tasks in SDNF, including satisfiability and forgetting, are tractable. The same work extends the approach to $C^\alpha \phi$5 through an alternating-operator variant (Fang et al., 2018). In planning terms, this supports polytime progression and restricted entailment checks once formulas are compiled into the target normal form.

Another route is semantic restriction. The commutativity-based framework augments $C^\alpha \phi$6 with the axiom

$C^\alpha \phi$7

for distinct agents, proves that the resulting epistemic planning problem is decidable, and derives a finitary non-fixpoint characterization of common knowledge. It also studies two generalizations: $C^\alpha \phi$8-commutativity, which remains decidable for two agents but becomes undecidable when $C^\alpha \phi$9 and $M=(S,\pi,R_1,\ldots,R_n)$0, and weak $M=(S,\pi,R_1,\ldots,R_n)$1-commutativity, for which plan existence in $M=(S,\pi,R_1,\ldots,R_n)$2–$M=(S,\pi,R_1,\ldots,R_n)$3 is decidable (Burigana et al., 2023).

Resource-bounded models yield further decidable fragments. In epistemic planning with attention, unrestricted attention action models lead to undecidability, but when actions are restricted to the No-Free-Lunch (NFL) class—where learning nontrivial information costs positive attention and all events are potentially distinguishable—plan existence becomes decidable. The proof relies on the finiteness of total attention and the fact that, once no further learning is possible, subsequent applications reduce to public-announcement behavior on a finite model (Belardinelli et al., 2021).

These results delimit a recurrent theme: full MEP inherits the expressiveness and hardness of DEL with nested epistemic attitudes, but tractability can emerge from compilation, semantic interaction axioms, bounded resources, or carefully restricted action templates.

5. Coordination, communication, and non-static epistemic settings

MEP is not limited to solving epistemic puzzles; it also formalizes coordination under partial and asymmetric information. In the implicit-coordination framework, a sequential plan is not merely a globally valid action sequence but one in which the owner of each action knows, from that agent’s current local perspective, that the action is applicable and that the remainder of the sequence will still succeed. This is captured through nested knowledge operators and perspective shifts. The “key-under-mat” example shows that a standard plan may fail as an implicitly coordinated plan because the acting agent cannot guarantee success from its local view, while the Russian card problem and the “MailTell” and “MailCheck” case studies provide empirical evidence that decentralized planning under distributed knowledge can be solved in this way (Engesser et al., 2017).

Communication is a particularly important class of epistemic action. In one DEL-based communication model, each communicative content is assigned an event in the action model, and communication is treated as an action that modifies the epistemic state of the team. The experimental evaluation uses Gridworld and Blocks World for Teams (BW4T), considers teams of size 3 and 4 across five scenarios, and measures completion time, total plan length, number of communications, and degree of sharedness. Averaged across scenarios, the Selective communication model reduces completion time by approximately $M=(S,\pi,R_1,\ldots,R_n)$4 and plan length by approximately $M=(S,\pi,R_1,\ldots,R_n)$5 versus No Communication in Gridworld, and by approximately $M=(S,\pi,R_1,\ldots,R_n)$6 and approximately $M=(S,\pi,R_1,\ldots,R_n)$7 in BW4T; in all environments, it achieves near-optimal action counts while often using $M=(S,\pi,R_1,\ldots,R_n)$8–$M=(S,\pi,R_1,\ldots,R_n)$9 fewer messages than Communication All (Alshehri et al., 2019).

More recent work extends MEP beyond static-environment assumptions. The Predictive Justified Perspective (PJP) model replaces the static retrieval rule of Justified Perspectives with predictive retrieval functions over processual variables, so that agents use past observations to predict changing variables. PJP is reported to solve all BBL instances optimally in under $(M,s)\models B_{ag_i}\phi$0 seconds, all Number instances except the unlearnable N1, and all seven Grapevine instances, while JP times out or fails on many higher-order and nonstatic cases (Li et al., 2024). Group Justified Perspectives (GJP) then extend justified belief to uniform belief, distributed belief, and common belief, with a finite-convergence fixed point for common belief and empirical planning times of $(M,s)\models B_{ag_i}\phi$1–$(M,s)\models B_{ag_i}\phi$2 seconds in adapted Number-domain instances requiring $(M,s)\models B_{ag_i}\phi$3 (Hu et al., 2024).

Other extensions treat epistemic resources explicitly. Attention-bounded DEL makes attention part of the state and action semantics (Belardinelli et al., 2021). A separate theoretical line studies belief revision in multi-agent systems by generalizing AGM and Darwiche–Pearl postulates to pointed Kripke models, giving both a generalized full-meet revision operator and an event-model-based revision operator, and showing that trade-offs arise when one asks for both one-shot AGM-style properties and strong iterated-revision principles (Thielscher et al., 4 May 2026).

6. Standardization, empirical systems, and emerging directions

As the field diversified, specification and evaluation became important research problems in their own right. E-PDDL was proposed as a standardized way of defining epistemic planning problems independently of solver architecture. Its syntax extends PDDL with epistemic belief formulas, action types ontic, sensing, and announcement, observer specifications, and bounded common-knowledge compilation. A reference parser translates E-PDDL domains and instances into planner-specific formats, including PDKB-PDDL for RP-MEP and MAR for EFP, and the stated motivation is to facilitate fair comparison, ensemble methods, and entry by new researchers (Fabiano et al., 2021).

Empirical comparisons across planners show no single dominant implementation strategy. On benchmarks from the literature—Selective Communication, Grapevine, Coin in the Box, Assembly Line, and Collaboration & Communication—PLATO’s multi-shot “many” configuration is generally fastest, grounding time is small relative to solve time, bisimulation checks in ASP can blow up grounding, and PLATO matches or outperforms EFP 2.0 on most domains of moderate plan length $(M,s)\models B_{ag_i}\phi$4 (Burigana et al., 2020). The Functional STRIPS approach reports that, in Corridor and Grapevine, its planner scales significantly better than the compared state-of-the-art compilation approach and remains expressive enough to handle continuous visibility and complex group-secrecy scenarios (Hu et al., 2019).

A current scalability direction is learned heuristic guidance over graph-structured epistemic states. GNN-derived heuristics treat Kripke structures as directed labeled graphs and learn estimates of distance to goal from solved instances. Across six standard MEP domains—Assembly Line, Collaboration & Communication, Coin in the Box, Epistemic Gossip, Grapevine, and Selective Communication—the reported gains include a $(M,s)\models B_{ag_i}\phi$5 reduction in node expansions on held-out test problems in per-domain training, reductions up to $(M,s)\models B_{ag_i}\phi$6 in Collaboration & Communication, a $(M,s)\models B_{ag_i}\phi$7 reduction on longer-horizon rich Selective Communication instances where BFS timed out on $(M,s)\models B_{ag_i}\phi$8 cases, and cross-domain transfer that cuts node counts by $(M,s)\models B_{ag_i}\phi$9 versus BFS (Briglia et al., 18 Aug 2025).

The scope of MEP is also expanding toward agentic AI systems. In LLM-based multi-agent systems, epistemic miscalibration in planning is defined as a latent and dynamic mismatch between subjective feasibility judgments and objective feasibility, and the proposed EPC-AW workflow combines Information-consistency-based Plan Selection with Consistency-guided Epistemic State Refinement. On six benchmarks—Bamboogle, 2Wiki, HotpotQA, Musique, GAIA, and MedQA—the reported system-level success improvement is an average of $\phi$0 (Wang et al., 22 May 2026). This suggests that the core MEP concern—planning under structured uncertainty about one’s own and others’ informational states—remains operative even when the underlying agents are not classical symbolic reasoners.

Across these developments, MEP has evolved from a DEL-grounded planning problem into a broader research area spanning Kripke and possibility semantics, action-model update, perspective-based belief reconstruction, declarative and compiled solvers, standardized modeling languages, and learned search guidance. The unifying technical issue is unchanged: plans must account for both how the world changes and how informational attitudes change, often at higher orders and across multiple interacting agents.