Man Muss Immer Umkehren
Johan van Benthem

Abstract:
Choosing a semantics validates certain axioms. But as the 
19th century German geometrist Jakobi said already: "One 
Should Always Convert'. Modal correspondences are a way 
of stepping back from statements of validity, and asking
the converse question 'what sort of models would make the 
given axiom valid'. Analyzing a sequence of well-known 
principles using standard correspondence techniques for
pure modal logic, we find the bare mechanics of the 
models for systems that superficially look different: 
spatial and temporal geometry, dynamic-epistemic update, 
and eventually even first-order predicate logic itself. 
The result of the correspondence analysis is often a 
generalized class of models over which even new logics 
can arise, which are of interest by themselves.