Mereological bimodal logics

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, square phi reads all the parts (of the current object) are phi, 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.