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DOI: 10.4230/LIPIcs.CONCUR.2023.34

Modal Logics for Mobile Processes Revisited

Authors: Tiange Liu, Alwen Tiu, and Jim de Groot

Published in: LIPIcs, Volume 279, 34th International Conference on Concurrency Theory (CONCUR 2023)

Abstract

We revisit the logical characterisations of various bisimilarity relations for the finite fragment of the π-calculus. Our starting point is the early and the late bisimilarity, first defined in the seminal work of Milner, Parrow and Walker, who also proved their characterisations in fragments of a modal logic (which we refer to as the MPW logic). Two important refinements of early and late bisimilarity, called open and quasi-open bisimilarity, respectively, were subsequently proposed by Sangiorgi and Walker. Horne, et. al., showed that open and quasi-bisimilarity are characterised by intuitionistic modal logics: OM (for open bisimilarity) and FM (for quasi-open bisimilarity). In this work, we attempt to unify the logical characterisations of these bisimilarity relations, showing that they can be characterised by different sublogics of a unifying logic. A key insight to this unification derives from a reformulation of the four bisimilarity relations (early, late, open and quasi-open) that uses an explicit name context, and an observation that these relations can be distinguished by the relative scoping of names and their instantiations in the name context. This name context and name substitution then give rise to an accessibility relation in the underlying Kripke semantics of our logic, that is captured logically by an S4-like modal operator. We then show that the MPW, the OM and the FM logics can be embedded into fragments of our unifying classical modal logic. In the case of OM and FM, the embedding uses the fact that intuitionistic implication can be encoded in modal logic S4.

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Tiange Liu, Alwen Tiu, and Jim de Groot. Modal Logics for Mobile Processes Revisited. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{liu_et_al:LIPIcs.CONCUR.2023.34,
  author =	{Liu, Tiange and Tiu, Alwen and de Groot, Jim},
  title =	{{Modal Logics for Mobile Processes Revisited}},
  booktitle =	{34th International Conference on Concurrency Theory (CONCUR 2023)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-299-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{279},
  editor =	{P\'{e}rez, Guillermo A. and Raskin, Jean-Fran\c{c}ois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.34},
  URN =		{urn:nbn:de:0030-drops-190289},
  doi =		{10.4230/LIPIcs.CONCUR.2023.34},
  annote =	{Keywords: pi-calculus, modal logic, intuitionistic logic, bisimilarity}
}

Document

DOI: 10.4230/LIPIcs.CALCO.2019.7

Coalgebraic Geometric Logic

Authors: Nick Bezhanishvili, Jim de Groot, and Yde Venema

Published in: LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

Abstract

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor T on some full subcategory of the category Top of topological spaces and continuous functions. We compare the notions of modal equivalence, behavioural equivalence and bisimulation on the resulting class of models, and we provide a final object for the corresponding category. Furthermore, we specify a method of lifting an endofunctor on Set, accompanied by a collection of predicate liftings, to an endofunctor on the category of topological spaces.

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Nick Bezhanishvili, Jim de Groot, and Yde Venema. Coalgebraic Geometric Logic. In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bezhanishvili_et_al:LIPIcs.CALCO.2019.7,
  author =	{Bezhanishvili, Nick and de Groot, Jim and Venema, Yde},
  title =	{{Coalgebraic Geometric Logic}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Roggenbach, Markus and Sokolova, Ana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.7},
  URN =		{urn:nbn:de:0030-drops-114354},
  doi =		{10.4230/LIPIcs.CALCO.2019.7},
  annote =	{Keywords: Coalgebra, Geometric Logic, Modal Logic, Topology}
}

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Modal Logics for Mobile Processes Revisited

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Coalgebraic Geometric Logic

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