MEREOLOGICAL BIMODAL LOGICS
Dazhu Li, Yanjing Wang · The Review of Symbolic Logic · 2022
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 $ readsall the parts(of the current object)are $\varphi $ , interpreted on the models with awhole-partbinary 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.