Easy problems are sometimes hard
Artificial Intelligence
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
ACM Computing Surveys (CSUR)
A logic-based theory of deductive arguments
Artificial Intelligence
Logic for Problem Solving
A Reasoning Model Based on the Production of Acceptable Arguments
Annals of Mathematics and Artificial Intelligence
On the computational complexity of assumption-based argumentation for default reasoning
Artificial Intelligence
Defeasible logic programming: an argumentative approach
Theory and Practice of Logic Programming
Dialectic proof procedures for assumption-based, admissible argumentation
Artificial Intelligence
Elements of Argumentation
Argue tuProlog: A Lightweight Argumentation Engine for Agent Applications
Proceedings of the 2006 conference on Computational Models of Argument: Proceedings of COMMA 2006
An algorithm to compute minimally grounded and admissible defence sets in argument systems
Proceedings of the 2006 conference on Computational Models of Argument: Proceedings of COMMA 2006
Algorithms for effective argumentation in classical propositional logic: a connection graph approach
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
An argumentation-based approach to handling inconsistencies in DL-Lite
KI'09 Proceedings of the 32nd annual German conference on Advances in artificial intelligence
Algorithms for generating arguments and counterarguments in propositional logic
International Journal of Approximate Reasoning
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Classical propositional logic is an appealing option for modelling argumentation but the computational viability of generating an argument is an issue. Here we propose ameliorating this problem by harnessing the notion of a connection graph to reduce the search space when seeking all the arguments for a claim from a knowledgebase. For a set of clauses, a connection graph is a graph where each node is a clause and each arc denotes that there exist complementary disjuncts in the pair of nodes. For a set of formulae in conjunctive normal form, we use the notion of the connection graph for the set of clauses obtained from the conjuncts in the formulae. When seeking arguments for a claim, we can focus our search on a particular subgraph of the connection graph that we call the focal graph. Locating this subgraph is relatively inexpensive in terms of computational cost. In addition, using (as the search space) the formulae of the initial knowledgebase, whose conjuncts relate to this subgraph, can substantially reduce the cost of looking for arguments. 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.