A General Katsuno-Mendelzon-Style Characterization of AGM Belief Base Revision for Arbitrary Monotonic Logics
This work provides a foundational extension of belief revision theory, addressing a theoretical gap for researchers in logic and AI, though it appears incremental as it builds directly on established KM and AGM frameworks.
The paper tackles the problem of generalizing the Katsuno-Mendelzon characterization of AGM belief base revision from propositional logic to arbitrary monotonic logics, achieving a representation theorem using total but non-transitive preference relations and identifying conditions for strengthening it to preorder assignments.
The AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. We generalize the approach of Katsuno and Mendelzon (KM) for characterizing AGM base revision from propositional logic to the setting of (multiple) base revision in arbitrary monotonic logics. Our core result is a representation theorem using the assignment of total - yet not transitive - "preference" relations to belief bases. We also provide a characterization of all logics for which our result can be strengthened to preorder assignments (as in KM's original work).