Tech Reports

ULCS-08-007

Taking the A-chain: Strict and Defeasible Implication in Argumentation Frameworks

Adam Wyner and Trevor Bench-Capon

Abstract

arguments as well as related complexity questions. However, applications of AFs are often held to require that arguments be given a more concrete instantiation. One popular method of instantiation is to postulate a knowledge base comprising facts and rules (typically both strict and defeasible in a Defeasible Logic (DL)). Arguments will then be demonstrations of claims from this knowledge base, which often require subarguments to demonstrate intermediate claims. Such a method is natural and readily applicable to logic programming, but it has been observed to exhibit a number of problems since allowing nodes in the AF this degree of structure introduces additional relations among arguments. In this paper we offer a principled view on instantiating arguments which retains the appeal of AFs, allows reasoning with respect to knowledge bases, yet avoids these problems. We restrict what can appear as nodes in the AF to simple assertions of literals or rule names. In addition, the attack relation between literals and rule names is restricted. We can thus retain the appropriate level of abstraction of the nodes of the AF as well as identify arguments which represent demonstrations from the knowledge base as structures in the AF. In this way, structured arguments can be identified in our framework as chains of these simpler arguments. The relations between these structured arguments which give rise to problems are now handled properly in the terms of which parts of the chain attack each other. Moreover, defeasible inference can be distinguished from strict inference by considering the attack relations within these chains. By restricting nodes of AFs, the theoretical and computational benefits can be retained, while the desired structured arguments are captured by structures superimposed on the AF. Our formalism provides a bridge between a deductive theory and AFs.

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