Abstract
Epistemic Logic (EL) successfully models epistemic and doxastic attitudes of agents and groups in multi-agent systems, including distributed systems, via relational structures called Kripke models. Dynamic Epistemic Logic (DEL) adds communication in the form of model-transforming updates. Private communication is key in distributed systems as processes exchanging (potentially corrupted) information about their private local state may not be detectable by any other process. This focus on privacy clashes with the fact that updates are applied to the whole Kripke model, which is usually commonly known by all agents, potentially leading to information leakage. To avoid information leakage and to minimize the corruption of local states resulting from faulty information, we introduce a special stratified structure for Kripke models using a privatization operation that explicitly breaks the common knowledge of the model. To represent agent-to-agent communication we introduce a novel leakage-free update mechanism for solving the consistent update synthesis task: design an update that makes a given goal formula true while maintaining the consistency of agents’ beliefs, if possible.
Supported by the Austrian Science Fund (FWF) projects ByzDEL (P33600) and Digital Modeling of Asynchronous Integrated Circuits (P32431-N30).
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Notes
- 1.
- 2.
A Kripke model (without an explicit point) is simply defined as \(\mathcal {M}= \langle S, R, V\rangle \).
- 3.
If \(vR_i u\) and \(uR_i w\), then \(vR_i w\).
- 4.
If \(vR_i u\) and \(vR_i w\), then \(uR_i w\).
- 5.
For every state v and agent i, there exists a state \(v'\) such that \(vR_iv'\).
- 6.
This restriction on the kind of allowed goal formulas is very natural for full-information protocols, wherein agents communicate all the beliefs they have accumulated.
- 7.
A cluster is a totally connected subset of worlds.
- 8.
Directed acyclic graph.
- 9.
Indeed, belief privatization graphs act as action models with additional privatization properties, and Algorithm 1 ensures that these properties are transferred into the resulting Kripke model. An approach using only action models, while possible, is not necessarily simpler, especially for planned future work with more complex goal formulas.
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Acknowledgments
We are grateful to Hans van Ditmarsch, Stephan Felber, Kristina Fruzsa, Rojo Randrianomentsoa, Hugo Rincón Galeana for multiple illuminating and inspiring discussions and additionally to Ulrich Schmid for his encouragement and inexhaustible optimism. We also thank the anonymous reviewers for their helpful comments and suggestions.
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Cignarale, G., Kuznets, R., Schlögl, T. (2024). Minimizing Agents’ State Corruption Resulting from Leak-Free Epistemic Communication Modeling. In: Meier, A., Ortiz, M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2024. Lecture Notes in Computer Science, vol 14589. Springer, Cham. https://doi.org/10.1007/978-3-031-56940-1_9
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