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

Vasiliki Efstathiou, Anthony Hunter
Lecture Notes in Computer Science  
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 logicbased 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 provide different definitions for consistency and entailment and hence give us different options for
more » ... ion. 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. Definition 6. Let φ and ψ be clauses. If Preattacks(φ, ψ) = {β} for some β, then Hence, the Preattacks relation is defined for any pair of clauses φ, ψ while the Attacks relation is defined for a pair of clauses φ, ψ such that |Preattacks(φ, ψ)| = 1
doi:10.1007/978-3-540-77684-0_19 dblp:conf/foiks/EfstathiouH08 fatcat:tib6gwweyzbydmmjkldlmtcxzi