Axiomatizability of propositionally quantified modal logics on relational frames

Journal article


Fritz, Peter. (2022). Axiomatizability of propositionally quantified modal logics on relational frames. The Journal of Symbolic Logic. pp. 1-36. https://doi.org/10.1017/jsl.2022.79
AuthorsFritz, Peter
Abstract

Propositional modal logic over relational frames is naturally extended with propositional quantifiers by letting them range over arbitrary sets of worlds of the relevant frame. This is also known as second-order propositional modal logic. The propositionally quantified modal logic of a class of relational frames is often not axiomatizable, although there are known exceptions, most notably the case of frames validating the strong modal logic S5 . Here, we develop new general methods with which many of the open questions in this area can be answered. We illustrate the usefulness of these methods by applying them to a range of examples, which provide a detailed picture of which normal modal logics define classes of relational frames whose propositionally quantified modal logic is axiomatizable. We also apply these methods to establish new results in the multimodal case.

Keywordspropositional quantifiers; modal logic; second-order propositional modal logic; axiomatizability; decidability; complexity
Year2022
JournalThe Journal of Symbolic Logic
Journal citationpp. 1-36
PublisherCambridge University Press
ISSN1943-5886
Digital Object Identifier (DOI)https://doi.org/10.1017/jsl.2022.79
Scopus EID2-s2.0-85143856629
Open accessPublished as ‘gold’ (paid) open access
Page range1-36
Publisher's version
License
File Access Level
Open
Output statusPublished
Publication dates
Online28 Nov 2022
Publication process dates
Deposited17 May 2023
Additional information

© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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.

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https://acuresearchbank.acu.edu.au/item/8z07v/axiomatizability-of-propositionally-quantified-modal-logics-on-relational-frames

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