Explainable Belief Harmonization under Dynamic Epistemic Partitions
Authors: Adam Kostka, Jarosław A. Chudziak
Organizations: Warsaw University of Technology · Warsaw University of Technology, Warsaw, Poland
Abstract
Existing approaches to multi-agent belief combination have established mature foundations for combining uncertain beliefs under common assumptions: consensus methods use iterative averaging, logic-based methods resolve conflicting knowledge bases, and epistemic logic analyzes agents' information states. Typically, these approaches assume that the structure determining what each agent can represent remains fixed. However, in many scenarios, agents gain or lose observational capacity during execution, and what was once admissible may become structurally impossible. This paper presents a formal framework for handling such runtime changes in epistemic partitions over continuous belief profiles. A hybrid approach exploits the advantages of answer set programming in elaboration tolerance, declarative integrity constraints, and explanations, with the numerical flexibility of Python. The framework applies to domains where agents operate at heterogeneous and possibly changing levels of resolution, and provides formal guarantees of admissibility preservation under refinement, unique mass-preserving repair under coarsening, and explanation completeness. Evaluation across 100 randomly generated topology changes confirms complete violation detection and explanation coverage.
We investigate the belief revision problem in epistemic planning, i.e., what will be the beliefs of all agents in a multi-agent system after an agent gains the belief in some state property. Based on the standard representation in epistemic planning of agents' beliefs via a single multi-agent Kripke model, we generalize the classical AGM belief revision postulates to the multi-agent setting, with the aim to provide a formal framework for evaluating dynamic epistemic reasoning frameworks in which the beliefs of all agents as the result of actions are computed. As an example of a simple operator that satisfies all of the generalized AGM postulates, we present generalized full-meet multi-agent belief revision. We moreover define a generalization of the standard postulates for iterated revision, present a more sophisticated, event model based revision operator, and discuss the potential issues in defining an epistemic operator on Kripke models that can satisfy all of the generalized postulates for iterated multi-agent belief revision.
Distributed agents in real-world settings frequently must coordinate under uncertainty with only partial observations. Coordination is necessary to share beliefs to aid in task completion, but communication costs bandwidth, introduces latency, and if done poorly, can degrade collective reasoning. This tension is especially acute in bandwidth-constrained deployments such as distributed sensing networks, autonomous reconnaissance, and collaborative cyber defense, where excessive transmission carries direct operational costs. Existing work has focused on multi-agent exploration and communication strategies, but not on how communication frequency and content jointly shape the collective belief state. Central to this challenge is the degree to which agents maintain compatible internal beliefs about the environment, a property we term \textit{epistemic alignment}. When agents share beliefs effectively, they converge on correct hypotheses; when communication is poorly designed, agents may converge confidently on wrong ones. We formalize this distinction and show it is not detectable from coordination metrics alone such as Jensen-Shannon Divergence or rate to consensus.
In distributed systems, the classical State Machine Replication (SMR) model assumes that correct replicas execute deterministic transitions to yield identical bitwise states. However, the rise of agentic distributed systems -- where autonomous, stochastic, and model-driven agents orchestrate infrastructure -- presents scenarios where deterministic, bitwise replication is insufficient. Replicas operating with generative models may exhibit divergent reasoning paths, summaries, and token boundaries, yet reach semantically equivalent and correct operational decisions. Forcing bitwise agreement across these stochastic participants degrades execution flexibility, induces context amnesia, and limits performance. We argue that in such settings replicas should agree on belief, not bits. We propose Epistemic State Replication (ESR), a belief-replication layer for agentic distributed systems that shifts the replication boundary from data visibility to knowledge visibility. We formalize the epistemic node state as a pair K = (L, B) separating the deterministic, immutable evidence log (L) from the stochastic, evolving belief lineage (B). To govern execution safety, we define Semantic Linearizability, which requires operations to reflect the latest committed operational meaning within a verifier-bounded semantic compatibility metric, and Bounded Eventual Coherence, which bounds expected semantic divergence under fair delivery, monotonic evidence, bounded verifier disturbance, and a contractive graft operator. We outline protocols for propagating derived insights using structured epistemic deltas, and formalize Verifiable Semantic Rollbacks to prune faulty premises from belief lineages without inducing context amnesia. We prototype ESR and report preliminary simulation results that show feasibility under the stated assumptions and illustrate reductions in secondary cognitive faults.