Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

Klein, Dominik; Rendsvig, Rasmus K.

doi:10.1007/978-3-662-55665-8_8

Cited by 8 publications

(8 citation statements)

References 36 publications

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“…A main result here is that Stone-like topologies are characterized by a logical convergence criterion, providing an argument for their naturalness. This results strengthens a result of [31]. Further, standard modal logics are used to exemplify discrete, imperfect, and perfect spaces, including relations to the Cantor set .…”

Section: Introductionsupporting

confidence: 81%

Metrics for Formal Structures, With an Application to Kripke Models and Their Dynamics

Klein¹,

Rendsvig²

2022

J. symb. log.

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The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems.

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Section: Introductionsupporting

confidence: 81%

Metrics for Formal Structures, With an Application to Kripke Models and Their Dynamics

Klein¹,

Rendsvig²

2022

J. symb. log.

Self Cite

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“…This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 8 Some very recent work goes towards this direction: [7] investigates the logic of oscillations, [30] defines model transformers for DEL dynamical systems with limit cycles while [21,22,31] and investigates their convergence and recurrence properties, and [12] proposes an epistemic logic for unadoptable behavior.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks

et al. 2018

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We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this diffusion policy, threshold models develop dynamically towards a guaranteed fixed point. We construct a minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors' behavior allows agents to anticipate changes in behavior of their closer neighbors. Overall, our logical formalism captures the interplay between the epistemic and social dimensions in social networks.

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“…The choice to use a proof-theoretic over a semantic quotient is motivated by general applicability: The notion of a sound logic in a language evaluated over a set of structures is conceptually uniform, while the semantic concept characterizing structural identity suited to the language in question may be highly variable. 5 In so doing, we follow [17] in referring to modal spaces:…”

Section: Modal Spacesmentioning

confidence: 99%

Metrics for Formal Structures, with an Application to Kripke Models and their Dynamics

Klein¹,

Rendsvig²

2017

Preprint

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This paper introduces and investigates a family of metrics on sets of structures for formal languages, with a special focus on their application to sets of pointed Kripke models and modal logic, and, in extension, to dynamic epistemic logic. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or semantic structures. We first study the topological properties of the resulting metric spaces. A key result provides sufficient conditions for spaces having the Stone property, i.e., being compact, totally disconnected and Hausdorff. Second, we turn to mappings, where it is shown that a widely used type of model transformations, product updates, give rise to continuous maps in the induced topology.

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Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

Cited by 8 publications

References 36 publications

Metrics for Formal Structures, With an Application to Kripke Models and Their Dynamics

Metrics for Formal Structures, With an Application to Kripke Models and Their Dynamics

Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks

Metrics for Formal Structures, with an Application to Kripke Models and their Dynamics

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