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Argumentation Mining (AM) aims to extract argumentative structures from texts by identifying argumentation components (ACs) and their argumentative relations (ARs). While previous works focus on representation learning to encode ACs and AC pairs, they fail to explicitly model the underlying reasoning patterns of AM, resulting in limited interpretability. This paper proposes a novel ̲First- ̲Order ̲Logic reasoning framework for ̲AM (FOL-AM), designed to explicitly capture logical reasoning paths within argumentative texts. By interpreting multiple AM subtasks as a unified relation query task modeled using FOL rules, FOL-AM facilitates multi-hop relational reasoning and enhances interpretability. The framework supports two flexible implementations: a fine-tuned approach to leverage task-specific learning, and a prompt-based method utilizing large language models to harness their generalization capabilities. Extensive experiments on two AM benchmarks demonstrate that FOL-AM outperforms strong baselines while significantly improving explainability.