Since Aristotle, logic has been conceived both as the foundation of demonstrative science and as a tool for dialectical reasoning in contexts of disagreement and uncertainty. This double role, often neglected in the modern formal tradition, has re-emerged with force in contemporary Artificial Intelligence, where logic is no longer confined to the axiomatic reconstruction of mathematics, but is increasingly used to model argument, dialogue, and rational deliberation among resource-bounded agents.

In this talk I will trace a trajectory from classical logic through the theory of abstract argumentation to recent work on dialectical models that account for real-world reasoning. I will show how logical tools can represent not only proofs but also conflicts, counterarguments, and defeasibility—features essential to scientific practice, political deliberation, and everyday reasoning.

A key challenge, however, is computational complexity. Standard frameworks assume that all possible arguments from a base can be constructed and evaluated, but this quickly becomes infeasible even in the propositional case. Depth-bounded reasoning offers a principled response: by limiting the depth of arguments that need to be generated, we obtain a tractable procedure that still preserves rationality postulates. Each increase in depth expands the inferential power of the system, mirroring the way human and artificial agents gradually extend their reasoning capacities under resource constraints.

The guiding theme is that computation allows us to revisit logic’s ancient vocation: to serve both as a science of valid inference and as a practical art of disputation. I will argue that this dialectical perspective opens new possibilities for the philosophy of computing, by clarifying how rationality can be preserved when agents reason with limited resources, conflicting evidence, and evolving commitments.