Given the increasingly dynamic nature of knowledge in the era of Web-based information exchange, techniques to revise recorded knowledge – such as knowledge graphs or ontologies – with respect to new findings are more important than ever. For knowledge representation approaches based on formal logics, the AGM belief revision postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K &M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. We generalize K &M’s approach to (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”; such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. We also provide a characterization of all Tarskian logics for which our result can be strengthened to assignments producing transitive preference relations as in K &M’s original work.