Elucidating Arguments Maps in Propositional Logic: Addressing Enthymemes and their Relationships

To better understand, and analyse, natural language arguments, it is desirable to represent them as logical arguments. However, most real-world arguments are enthymemes (i.e. some of the premises and/or claims are implicit), and therefore, there is a need to identify these implicit aspects. A ramification of this is that we may then need to edit some of the explicit premises and/or claim to remove redundant aspects and/or to allow the newly identified implicit formulae to work correctly with the explicit formulae. Furthermore, we may need to edit the claim so that it correctly attacks or supports other arguments as predicted by argument mining or as required by the user. To address these requirements, we propose a logic-based framework, based on classical propositional logic, for representing enthymemes, and manipulating them through a range of logical operations. We introduce meta-level rules to manipulate arguments (e.g. to add or delete premises, to edit claims, to split an argument into two arguments, and to merge two arguments into one). In order to direct the use of meta-level rules, we also introduce gain measures. When choosing a sequence of meta-level rules to apply, we can choose those that increase gain. This meta-level reasoning framework provides some clarity on the nature of enthymemes, and on how agents might elucidate them through a transparent and incremental process.