Knowledgebase Compilation for Efficient Logical Argumentation

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 are based on different definitions for entailment and consistency, and give us different options for argumentation. For a variety of logics, in particular for classical logic, the computational viability of generating arguments is an issue. Here, we present a solution that involves compiling a knowledgebase ∆ based on the set of minimal inconsistent subsets of ∆, and then generating arguments from the compilation. Whilst generating a compilation is expensive, generating arguments from a compilation is relatively inexpensive.