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A MODULAR BISIMULATION CHARACTERISATION FOR FRAGMENTS OF HYBRID LOGIC

Part of: Model theory General logic Theory of computing

Published online by Cambridge University Press:  03 March 2025

GUILLERMO BADIA Open the ORCID record for GUILLERMO BADIA [Opens in a new window] ,
DANIEL GĂINĂ Open the ORCID record for DANIEL GĂINĂ [Opens in a new window] ,
ALEXANDER KNAPP ,
TOMASZ KOWALSKI Open the ORCID record for TOMASZ KOWALSKI [Opens in a new window]  and
MARTIN WIRSING
GUILLERMO BADIA*
Affiliation:
SCHOOL OF HISTORICAL AND PHILOSOPHICAL INQUIRY UNIVERSITY OF QUEENSLAND BRISBANE, QLD, AUSTRALIA
DANIEL GĂINĂ
Affiliation:
INSTITUTE OF MATHEMATICS FOR INDUSTRY KYUSHU UNIVERSITY FUKUOKA, JAPAN E-mail: daniel@imi.kyushu-u.ac.jp
ALEXANDER KNAPP
Affiliation:
INSTITUTE OF COMPUTER SCIENCE UNIVERSITY OF AUGSBURG AUGSBURG, GERMANY E-mail: knapp@informatik.uni-augsburg.de
TOMASZ KOWALSKI
Affiliation:
DEPARTMENT OF LOGIC, INSTITUTE OF PHILOSOPHY JAGIELLONIAN UNIVERSITY KRAKÓW, POLAND SCHOOL OF MATHEMATICAL AND PHYSICAL SCIENCES LA TROBE UNIVERSITY, MELBOURNE VIC, AUSTRALIA and SCHOOL OF HISTORICAL AND PHILOSOPHICAL INQUIRY UNIVERSITY OF QUEENSLAND BRISBANE, QLD, AUSTRALIA E-mail: tomasz.s.kowalski@uj.edu.pl
MARTIN WIRSING
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE LUDWIG-MAXIMILIANS-UNIVERSITY MUNICH MUNICH, GERMANY E-mail: wirsing@lmu.de
*
E-mail: g.badia@uq.edu.au
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Abstract

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There are known characterisations of several fragments of hybrid logic by means of invariance under bisimulations of some kind. The fragments include $\{\mathord {\downarrow }, \mathord {@}\}$ with or without nominals (Areces, Blackburn, Marx), $\mathord {@}$ with or without nominals (ten Cate), and $\mathord {\downarrow }$ without nominals (Hodkinson, Tahiri). Some pairs of these characterisations, however, are incompatible with one another. For other fragments of hybrid logic no such characterisations were known so far. We prove a generic bisimulation characterisation theorem for all standard fragments of hybrid logic, in particular for the case with $\mathord {\downarrow }$ and nominals, left open by Hodkinson and Tahiri. Our characterisation is built on a common base and for each feature extension adds a specific condition, so it is modular in an engineering sense.

Keywords

hybrid logicbisimulationsvan Benthem characterisation

MSC classification

Primary: 03B45: Modal logic (including the logic of norms) 03C07: Basic properties of first-order languages and structures 68Q85: Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)

Information

Type
Article
Information
Bulletin of Symbolic Logic , Volume 31 , Issue 4 , December 2025 , pp. 590 - 618
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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