3 papers
math.LO2024
Hybrid logic for strict betweenness
Rafał Gruszczyński, Zhiguang Zhao
The paper is devoted to modal properties of the ternary strict betweenness relation as used in the development of various systems of geometry. We show that such a relation is non-d…
math.LO2023
The sum relation as a primitive concept of mereology
Rafal Gruszczynski, Dazhu Li
Mereology in its formal guise is usually couched in a language whose signature contains only one primitive binary predicate symbol representing the part of relation, either the pro…
math.LO2023
Betweenness algebras
Ivo Duentsch, Rafal Gruszczynski, Paula Menchon
We introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms fo…