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MEREOLOGICAL BIMODAL LOGICS

Part of: Model theory General logic Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  27 January 2022

DAZHU LI Open the ORCID record for DAZHU LI [Opens in a new window]  and
YANJING WANG Open the ORCID record for YANJING WANG [Opens in a new window]
DAZHU LI
Affiliation:
INSTITUTE OF PHILOSOPHY CHINESE ACADEMY OF SCIENCES BEIJING, CHINA and DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CHINESE ACADEMY OF SCIENCES BEIJING, CHINA E-mail [email protected]
YANJING WANG
Affiliation:
INSTITUTE OF FOREIGN PHILOSOPHY AND DEPARTMENT OF PHILOSOPHY PEKING UNIVERSITY BEIJING, CHINA E-mail: [email protected]
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Abstract

In this paper, using a propositional modal language extended with the window modality, we capture the first-order properties of various mereological theories. In this setting, $\Box \varphi $ reads all the parts (of the current object) are $\varphi $, interpreted on the models with a whole-part binary relation under various constraints. We show that all the usual mereological theories can be captured by modal formulas in our language via frame correspondence. We also correct a mistake in the existing completeness proof for a basic system of mereology by providing a new construction of the canonical model.

Keywords

mereologymodal logicwindow modalitycorrespondence

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03A05: Philosophical and critical 03C80: Logic with extra quantifiers and operators 03C07: Basic properties of first-order languages and structures
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 4 , December 2022 , pp. 823 - 858
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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