Question answering agents in long-term conversations must reason over massive, temporally dispersed dialogue histories. However, existing memory mechanisms primarily treat past information as \textit{passively} stored facts, leading to semantic gaps and unreliable reasoning. To address this limitation, we propose RuleMem, a rule-based memory framework that induces reusable logical rules from historical interactions to \textit{actively} guide both evidence retrieval and reasoning. Specifically, RuleMem constructs natural-language Horn clauses from conversations and validates them via a Rule Perplexity Consistency (RPC) mechanism. These induced rules enable the retrieval of semantically distant evidence while providing an explicit logical structure for answer generation. We conducted a comprehensive evaluation of RuleMem on two long-term conversational benchmarks, LoCoMo and LongMemEval_s*. In a rigorous comparison against 14 baselines on LoCoMo, RuleMem achieved the highest accuracy, exceeding the baseline average by 27.47 points (a 54.3% relative improvement).

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