Conversational LLM agents accumulate persistent state across sessions, but existing memory systems treat updates as append-or-replace heuristics, leaving contradictory beliefs to coexist in the store and forcing the answer model to reconcile them at query time. We argue this is the wrong abstraction: conversation is a stream of belief revisions, and the right formal lens is the Alchourrón–Gärdenfors–Makinson (AGM) framework, adapted to Hansson belief bases. We present , which operationalizes the AGM operator set as the write semantics of a history-preserving fact belief base. A uniform LLM-driven resolver classifies every extracted claim into one of four actions (exp, rev, dup, con) and runs at two timings: per round against the recent session, and across sessions over a similarity graph. The store never deletes; superseded beliefs retain predecessor pointers, and a context-selection step decides per query whether to surface the head, the full chain, or neither. On LoCoMo (1,540 questions) reaches 85.5% over Mem0-graph) and 92.3% with a stronger backbone. On BEAM (400 questions) it reaches 54.5% (+21.8 over the LIGHT mean).