Grounded Continuation: A Linear-Time Runtime Verifier for LLM Conversations

Abstract

In a long conversation, an LLM can produce a plausible continuation that rests on premises the conversation has already abandoned. No runtime check ties its output to what the conversation has established, a gap that context-manipulation attacks on deployed agents exploit. We close this gap with a runtime verifier: an LLM Interpreter classifies each utterance into one of eight epistemic operations, and a symbolic engine applies them to a dependency map that records what every claim rests on and whether it still stands. Whether a continuation is grounded reduces to a walk over the map, linear in its size, with no LLM call. Retraction propagates through the same map with a conflict-free guarantee, flagging exactly the conclusions that lose support. On ReviseQA for belief revision and MemoryAgentBench's fact-consolidation split, two third-party benchmarks where earlier premises are superseded, the verifier leads a budget-matched retrieval baseline across five QA models and lifts MemoryAgentBench single-hop accuracy from 0.46--0.95 to 0.93--0.98. With the verifier, even the 7B model overtakes unaided GPT-4o. These runs feed the engine the benchmarks' own structured updates. When a GPT-4o Interpreter extracts every update from raw text instead, accuracy is statistically unchanged. Per-query cost is flat in conversation length, prompts staying near 0.8k tokens where full context reaches 114k and retraction queries under a microsecond at 2000 turns.