  We establish a generic, model-theoretic characterization of belief revision
operators implementing the paradigm of minimal change according to the seminal
work by Alchourr\'{o}n, G\"{a}rdenfors, and Makinson (AGM). Our
characterization applies to all Tarskian logics, that is, all logics with a
classical model-theoretic semantics, and hence a wide variety of formalisms
used in knowledge representation and beyond, including many for which a
model-theoretic characterization has hitherto been lacking. Our starting point
is the approach by Katsuno and Mendelzon (K&M), who provided such a
characterization for propositional logic over finite signatures. We generalize
K&M's approach to the setting of AGM-style revision over bases in arbitrary
Tarskian logics, where base may refer to one of the various ways of
representing an agent's beliefs (such as belief sets, arbitrary or finite sets
of sentences, or single sentences). Our first core result is a representation
theorem providing a two-way correspondence between AGM-style revision operators
and specific assignments: functions associating every base to a "preference"
relation over interpretations, which must be total but is - in contrast to
prior approaches - not always transitive. As our second core contribution, we
provide a characterization of all logics for which our result can be
strengthened to assignments producing transitive preference relations (as in
K&M's original work). Alongside these main contributions, we discuss diverse
variants of our findings as well as ramifications for other areas of belief
revision theory.
