Coherence in finite argument systems

Abstract

Argument Systems provide a rich abstraction within which divers concepts of reasoning, acceptability and defeasibility of arguments, etc., may be studied using a unified framework. Two important concepts of the acceptability of an argument p in such systems are credulous acceptance to capture the notion that p can be ‘believed’; and sceptical acceptance capturing the idea that if anything is believed, then p must be. One important aspect affecting the computational complexity of these problems concerns whether the admissibility of an argument is defined with respect to ‘ preferred’ or ‘ stable’ semantics. One benefit of so-called ‘ coherent’ argument systems being that the preferred extensions coincide with stable extensions. In this note we consider complexity-theoretic issues regarding deciding if finitely presented argument systems modelled as directed graphs are coherent. Our main result shows that the related decision problem is Π 2 ( p) -complete and is obtained solely via the graph-theoretic representation of an argument system, thus independent of the specific logic underpinning the reasoning theory.