Topological Dualities for Modal Algebras
This work provides foundational insights into modal logic and topology, but it appears incremental as it builds on existing Stone-type dualities.
The paper tackles the problem of establishing dualities between categories of modal algebras and relational spaces, showing how different morphisms affect point constructions and simplifying correspondences for semicontinuous relations.
We display a family of Stone-type dualities linking categories of frames carrying pairs of modal operators to categories of spaces carrying a binary relation. Different notions of morphism used on the relational side lead to significant variations in the point construction. We show how the situation simplifies in the case of semicontinuous relations, allowing for straightforward correspondences between modal axioms and relational properties.