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Invited Talk

DOI: 10.4230/LIPIcs.CSL.2025.4

Playing with Modalities (Invited Talk)

Authors: Elaine Pimentel, Carlos Olarte, Timo Lang, Robert Freiman, and Christian G. Fermüller

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract

In this work, we will explore modalities through dialogical game lenses. Games provide a powerful tool for bridging the gap between intended and formal semantics, often offering a more conceptually natural approach to logic than traditional model-theoretic semantics. We begin by exploring substructural calculi from a game semantic perspective, driven by intuitions about resource-consciousness and, more specifically, cost-sensitive reasoning. The game comes into full swing as we introduce cost labels to assumptions and a corresponding budget. Different proofs of the same end-sequent are interpreted as strategies for a player to defend a claim, which vary in cost. This leads to a labelled calculus, which can be viewed as a fragment of subexponential linear logic. We conclude this first part with a discussion of cut-admissibility for the proposed system. In the second part, we show that our games offer an interesting insight also into modal logics. More precisely, we will focus on the modal logic PNL, characterised by Kripke frames with two types of disjoint and symmetric reachability relations. This framework is motivated by the study of group polarisation, where the opinions or beliefs of individuals within a group become more extreme or polarised after interaction. Our approach to reasoning about group polarisation is based on PNL and highlights a different aspect of formal reasoning about the corresponding models - using games and proof systems. We conclude by outlining potential directions for future research.

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Elaine Pimentel, Carlos Olarte, Timo Lang, Robert Freiman, and Christian G. Fermüller. Playing with Modalities (Invited Talk). In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pimentel_et_al:LIPIcs.CSL.2025.4,
  author =	{Pimentel, Elaine and Olarte, Carlos and Lang, Timo and Freiman, Robert and Ferm\"{u}ller, Christian G.},
  title =	{{Playing with Modalities}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.4},
  URN =		{urn:nbn:de:0030-drops-227614},
  doi =		{10.4230/LIPIcs.CSL.2025.4},
  annote =	{Keywords: Linear logic, modal logic, proof theory, game semantics}
}

Document

DOI: 10.4230/LIPIcs.CSL.2015.94

Elementary Elimination of Prenex Cuts in Disjunction-free Intuitionistic Logic

Authors: Matthias Baaz and Christian G. Fermüller

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract

The size of shortest cut-free proofs of first-order formulas in intuitionistic sequent calculus is known to be non-elementary in the worst case in terms of the size of given sequent proofs with cuts of the same formulas. In contrast to that fact, we provide an elementary bound for the size of cut-free proofs for disjunction-free intuitionistic logic for the case where the cut-formulas of the original proof are prenex. Moreover, we establish non-elementary lower bounds for classical disjunction-free proofs with prenex cut-formulas and intuitionistic disjunction-free proofs with non-prenex cut-formulas.

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Matthias Baaz and Christian G. Fermüller. Elementary Elimination of Prenex Cuts in Disjunction-free Intuitionistic Logic. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 94-109, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{baaz_et_al:LIPIcs.CSL.2015.94,
  author =	{Baaz, Matthias and Ferm\"{u}ller, Christian G.},
  title =	{{Elementary Elimination of Prenex Cuts in Disjunction-free Intuitionistic Logic}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{94--109},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.94},
  URN =		{urn:nbn:de:0030-drops-54097},
  doi =		{10.4230/LIPIcs.CSL.2015.94},
  annote =	{Keywords: Cut-elimination, sequent calculus, intuitionistic logic}
}

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Documents authored by Fermüller, Christian G.

Playing with Modalities (Invited Talk)

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Elementary Elimination of Prenex Cuts in Disjunction-free Intuitionistic Logic

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