Algorithms for Effective Argumentation in Classical Propositional Logic: A Connection Graph Approach

Abstract

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 $\langle\Phi,\alpha\rangle$ 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. Here we propose ameliorating this problem by using connection graphs to give information on the ways that formulae of the knowledgebase can be used to minimally and consistently entail a claim. Using a connection graph allows for a substantially reduced search space to be used when seeking all the arguments for a claim from a knowledgebase. We provide a theoretical framework and algorithms for this proposal, together with some theoretical results and some preliminary experimental results to indicate the potential of the approach.