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DOI: 10.4230/OASIcs.TIME.2026.5

Social Networks Through Time: Completeness of Temporal Network Logic

Authors: Saúl Fernández González, Mina Young Pedersen, and Sonja Smets

Published in: OASIcs, Volume 146, 33rd International Symposium on Temporal Representation and Reasoning (TIME 2026)

Abstract

The framework of Temporal Network Logic (TNL) - first introduced in [Pedersen et al., 2021] and further developed in [Pedersen et al., 2023; Mina Young Pedersen, 2024] - was construed to model how a social network of interacting agents changes through time, with a language that could reflect both agents' actions, such as posting information and following each other, as well as temporal operators. This framework allows, among other things, to detect social bots, by modelling given bot behaviours as logical formulas and checking these formulas against a given model. While such applications were the main focus in [Pedersen et al., 2021; Pedersen et al., 2023; Mina Young Pedersen, 2024], the complete axiomatic system of this language has remained an open problem. In this paper, we focus on new logic-technical results and give a complete axiomatisation for TNL as well as a partial completeness result for its hybrid extension. The proofs are nonstandard and mix techniques from temporal and hybrid logics with "orthogonal" models.

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Saúl Fernández González, Mina Young Pedersen, and Sonja Smets. Social Networks Through Time: Completeness of Temporal Network Logic. In 33rd International Symposium on Temporal Representation and Reasoning (TIME 2026). Open Access Series in Informatics (OASIcs), Volume 146, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fernandezgonzalez_et_al:OASIcs.TIME.2026.5,
  author =	{Fern\'{a}ndez Gonz\'{a}lez, Sa\'{u}l and Pedersen, Mina Young and Smets, Sonja},
  title =	{{Social Networks Through Time: Completeness of Temporal Network Logic}},
  booktitle =	{33rd International Symposium on Temporal Representation and Reasoning (TIME 2026)},
  pages =	{5:1--5:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-448-2},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{146},
  editor =	{Orlandini, AndreA and Pinchinat, Sophie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.TIME.2026.5},
  URN =		{urn:nbn:de:0030-drops-277017},
  doi =		{10.4230/OASIcs.TIME.2026.5},
  annote =	{Keywords: temporal logic, completeness, social network logic, hybrid logic, logics for multi-agent systems}
}

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Social Networks Through Time: Completeness of Temporal Network Logic

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