Autonomous large language model (LLM) agents have shown strong potential for open-ended information-seeking tasks. However, existing agent frameworks primarily rely on sequential execution, making them vulnerable to error accumulation in long-horizon reasoning. Recent plan-and-execute approaches partially alleviate this issue, but their fixed planning strategies still struggle to recover from intermediate failures. We propose Logic Tree, a non-linear agentic reasoning framework formulated as a Directed Acyclic Graph (DAG). Instead of following a fixed plan with sequential execution, Logic Tree models complex task solving as a dynamically evolving and recoverable graph search process. The framework decomposes queries into parallel execution branches and incorporates a two-level self-correction mechanism. Local backtracking performs targeted rollback to repair failed reasoning states, while global replanning revises high-level execution strategies and preserves verified intermediate conclusions through a knowledge sanitation process. Experiments on BrowseComp, GAIA, and XBench show that Logic Tree consistently outperforms both sequential and plan-and-execute baselines. Further ablation studies demonstrate that combining DAG-based parallel execution with dynamic error recovery substantially improves robustness in long-horizon research tasks.