Neighbourhood Semantics for Graded Modal Logic

Jinsheng Chen; Hans van Ditmarsch; Giuseppe Greco; Apostolos  Tzimoulis

doi:10.18778/0138-0680.2021.12

Authors

Jinsheng Chen Zhejiang University, Department of Philosophy
Hans van Ditmarsch LORIA, CNRS, University of Lorraine https://orcid.org/0000-0003-4526-8687
Giuseppe Greco Vrije Universiteit Amsterdam, School of Business and Economics, Ethics, Governance and Society https://orcid.org/0000-0002-4845-3821
Apostolos Tzimoulis Vrije Universiteit Amsterdam, School of Business and Economics, Ethics, Governance and Society https://orcid.org/0000-0002-6228-4198

DOI:

https://doi.org/10.18778/0138-0680.2021.12

Keywords:

Graded modal logic, neighbourhood frames, bisimulation

Abstract

We introduce a class of neighbourhood frames for graded modal logic embedding Kripke frames into neighbourhood frames. This class of neighbourhood frames is shown to be first-order definable but not modally definable. We also obtain a new definition of graded bisimulation with respect to Kripke frames by modifying the definition of monotonic bisimulation.

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