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MEREOLOGICAL BIMODAL LOGICS

Published online by Cambridge University Press:  27 January 2022

DAZHU LI
Affiliation:
INSTITUTE OF PHILOSOPHY CHINESE ACADEMY OF SCIENCESBEIJING, CHINA and DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CHINESE ACADEMY OF SCIENCESBEIJING, CHINA E-mail lidazhu@ucas.ac.cn
YANJING WANG*
Affiliation:
INSTITUTE OF FOREIGN PHILOSOPHY AND DEPARTMENT OF PHILOSOPHY PEKING UNIVERSITYBEIJING, CHINA

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.

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

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