Algorithms for generating arguments and counterarguments in propositional logic

A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α〉〈Φ,α〉 where ΦΦ is minimal subset of the knowledgebase such that ΦΦ is consistent and ΦΦ entails the claim αα. Different logics provide different definitions for consistency and entailment and hence give us different options for formalising arguments and counterarguments. The expressivity of classical propositional logic allows for complicated knowledge to be represented but its computational cost is an issue. In previous work we have proposed addressing this problem using connection graphs and resolution in order to generate arguments for claims that are literals. Here we propose a development of this work to generate arguments for claims that are disjunctive clauses of more than one disjunct, and also to generate counteraguments in the form of canonical undercuts (i.e. arguments that with a claim that is the negation of the conjunction of the support of the argument being undercut).

Research Highlights
► This paper provides the first practical algorithms, together the necessary theoretical developments.
► For generating classical logic arguments with claims that are clauses.
► For generating classical logic arguments that are canonical undercuts.
► For generating argument trees with classical logic arguments.