This paper introduces a formal framework for modeling agentic agents in large-scale multi-agent systems (MAS), emphasizing their cognitive capabilities and autonomy dimensions—participation, goal, and execution autonomy. We define agentic agents as entities capable of higher-order reasoning, strategic planning, and social interaction, and demonstrate their reducibility to autonomous, goal-driven, and reactive agents through structured mathematical mappings. By formalizing autonomy, we enable reuse of existing MAS algorithms and coordination protocols, avoiding redundant system design. The proposed abstractions support scalable, ethically aligned, and cognitively aware agent architectures suitable for dynamic, decentralized environments.