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.