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Documents authored by Bellier, Dylan


Document
Plan Logic

Authors: Dylan Bellier, Massimo Benerecetti, Fabio Mogavero, and Sophie Pinchinat

Published in: LIPIcs, Volume 323, 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)


Abstract
When reasoning about games, one is often interested in verifying more intricate strategic properties than the mere existence of a winning strategy for a given coalition. Several languages, among which the very expressive Strategy Logic (SL), have been proposed that explicitly quantify over strategies in order to express and verify such properties. However, quantifying over strategies poses serious issues: not only does this lead to a non-elementary model-checking problem, but the classic Tarskian semantics is not fully adequate, both from a conceptual and practical viewpoint, since it does not guarantee the realisability of the strategies involved. In this paper, we follow a different approach and introduce Plan Logic (PL), a logic that takes plans, i.e., sequences of actions, as first-class citizens instead of strategies. Since plans are much simpler objects than strategies, it becomes easier to enforce realisability. In this setting, we can recover strategic reasoning by means of a compositional hyperteams semantics, inspired by the well-known team semantics. We show that the Conjunctive-Goal and Disjunctive-Goal fragments of SL are captured by PL, with an effective polynomial translation. This result relies on the definition of a suitable game-theoretic semantics for the two fragments. We also investigate the model-checking problem for PL. For the full prenex fragment, the problem is shown to be fixed-parameter-tractable: it is polynomial in the size of the model, when the formula is fixed, and 2-ExpTimeC in the size of the formula. For the Conjunctive-Goal and Disjunctive-Goal fragments of PL this result can be improved to match the optimal polynomial complexity in the size of the model, regardless of the size of the formula.

Cite as

Dylan Bellier, Massimo Benerecetti, Fabio Mogavero, and Sophie Pinchinat. Plan Logic. In 44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 323, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{bellier_et_al:LIPIcs.FSTTCS.2024.9,
  author =	{Bellier, Dylan and Benerecetti, Massimo and Mogavero, Fabio and Pinchinat, Sophie},
  title =	{{Plan Logic}},
  booktitle =	{44th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2024)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-355-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{323},
  editor =	{Barman, Siddharth and Lasota, S{\l}awomir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2024.9},
  URN =		{urn:nbn:de:0030-drops-221988},
  doi =		{10.4230/LIPIcs.FSTTCS.2024.9},
  annote =	{Keywords: Logic for strategic reasoning, Strategy Logic, Realisable strategies, Strategies vs. plans, Hyperteam semantics}
}
Document
Dependency Matrices for Multiplayer Strategic Dependencies

Authors: Dylan Bellier, Sophie Pinchinat, and François Schwarzentruber

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)


Abstract
In multi-player games, players take their decisions on the basis of their knowledge about what other players have done, or currently do, or even, in some cases, will do. An ability to reason in games with temporal dependencies between players' decisions is a challenging topic, in particular because it involves imperfect information. In this work, we propose a theoretical framework based on dependency matrices that includes many instances of strategic dependencies in multi-player imperfect information games. For our framework to be well-defined, we get inspiration from quantified linear-time logic where each player has to label the timeline with truth values of the propositional variable she owns. We study the problem of the existence of a winning strategy for a coalition of players, show it is undecidable in general, and exhibit an interesting subclass of dependency matrices that makes the problem decidable: the class of perfect-information dependency matrices.

Cite as

Dylan Bellier, Sophie Pinchinat, and François Schwarzentruber. Dependency Matrices for Multiplayer Strategic Dependencies. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 31:1-31:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bellier_et_al:LIPIcs.FSTTCS.2022.31,
  author =	{Bellier, Dylan and Pinchinat, Sophie and Schwarzentruber, Fran\c{c}ois},
  title =	{{Dependency Matrices for Multiplayer Strategic Dependencies}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{31:1--31:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.31},
  URN =		{urn:nbn:de:0030-drops-174230},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.31},
  annote =	{Keywords: Temporal dependency, Delay games, Strategic reasoning, Temporal logic}
}
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