In this paper, we introduce A-BDI, the first metamodel for formal and computational argumentation. It contains three models, conceptualizing argumentation as balancing, argumentation as dialogue, and argumentation as inference respectively. Each model looks at argumentation from a different perspective, addressing its own concerns and using its own formal and computational methods. Whereas balancing is inspired by the scale metaphor and uses quantitative techniques typically found in theories in economics and neural computing, dialogue is developed in multiagent communication and interaction and uses chatbot and Large Language Models (LLMs) technology, and inference is derived from theoretical investigations in knowledge representation and reasoning and uses techniques from symbolic reasoning. By bringing together new and traditional Artificial Intelligence (AI) approaches, the A-BDI metamodel provides a formal and computational framework for human-level, neuro-symbolic, and hybrid AI.