There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logic-based argumentation is that an argument is a pair Φ, α where Φ is minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claim α. Different logics provide different definitions for consistency and entailment and hence give us different options for argumentation. Classical propositional logic is an appealing option for argumentation but the computational viability of generating an argument is an issue. To better explore this issue, we use quantified Boolean formulae to characterize an approach to argumentation based on classical logic.
Finally, in REF , in the context of logic-based argumentation, the authors use quantified Boolean formulae (QBFs) to characterize various problems (arguments, undercut, argument trees) in argumentation based on classical logic, and use them to obtain new computational complexity results.
Encoding Deductive Argumentation in Quantified Boolean Formulae
Artif. Intell.
Artif. Intell.
Mathematics Computer Science