Real Arguments Are Approximate Arguments

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. However, real arguments (i.e. arguments presented by humans) usually do not have enough explicitly presented premises for the entailment of the claim. This is because there is some common knowledge that can be assumed by a proponent of an argument and the recipient of it. This allows the proponent of an argument to encode an argument into a real argument by ignoring the common knowledge, and it allows a recipient of a real argument to decode it into an argument by drawing on the common knowledge. If both the proponent and recipient use the same common knowledge, then this process is straightforward. Unfortunately, this is not always the case, and raises the need for an approximation of the notion of an argument for the recipient to cope with the disparities between the different views on what constitutes common knowledge.