Computational properties of argument systems satisfying graph-theoretic constraints

One difficulty that arises in abstract argument systems is that many natural questions regarding argument acceptability are, in general, computationally intractable having been classified as complete for classes such as NP, co-NP, and  ¢¡£ . In consequence, a number of researchers have considered methods for specialising the structure of such systems so as to identify classes for which efficient decision processes exist. In this paper the effect of a number of graph-theoretic restrictions is considered: ¤ -partite systems (¤¦¥¨§ ) in which the set of arguments may be partitioned into ¤ sets each of which is conflict-free; systems in which the numbers of attacks originating from and made upon any argument are bounded; planar systems; and, finally, those of ¤ -bounded treewidth. For the class of bipartite graphs, it is shown that determining the acceptability status of a specific argument can be accomplished in polynomial-time under both credulous and sceptical semanti...

• Type: Journal
• Year: 2007
• Where: AI
• Authors: Paul E. Dunne
• Keywords: Abstract Argument Systems, AI 2007, Argument Acceptability, Artificial Intelligence, Systems