Semantical considerations on nonmonotonic logic
Artificial Intelligence
A logical framework for default reasoning
Artificial Intelligence
A mathematical treatment of defeasible reasoning and its implementation
Artificial Intelligence
Preferred extensions are partial stable models
Journal of Logic Programming
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Proceedings of the eleventh international conference on Logic programming
An abstract, argumentation-theoretic approach to default reasoning
Artificial Intelligence
Stable models and non-determinism in logic programs with negation
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Nonmonotonic Logic II: Nonmonotonic Modal Theories
Journal of the ACM (JACM)
Preferred Arguments are Harder to Compute than Stable Extension
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
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CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Synthesis of Proof Procedures for Default Reasoning
LOPSTR '96 Proceedings of the 6th International Workshop on Logic Programming Synthesis and Transformation
Towards efficient default reasoning
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
A system for defeasible argumentation, with defeasible priorities
Artificial intelligence today
Dialectic proof procedures for assumption-based, admissible argumentation
Artificial Intelligence
A dialectic procedure for sceptical, assumption-based argumentation
Proceedings of the 2006 conference on Computational Models of Argument: Proceedings of COMMA 2006
Basic influence diagrams and the liberal stable semantics
Proceedings of the 2008 conference on Computational Models of Argument: Proceedings of COMMA 2008
Dialectic proof procedures for assumption-based, admissible argumentation
Artificial Intelligence
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We define abstract proof procedures for performing credulous and sceptical non-monotonic reasoning, with respect to the argumentation-theoretic formulation of non-monotonic reasoning proposed in [1]. Appropriate instances of the proposed proof procedures provide concrete proof procedures for concrete formalisms for non-monotonic reasoning, for example logic programming with negation as failure and default logic.We propose (credulous and sceptical) proof procedures under different argumentation-theoretic semantics, namely the conventional stable model semantics and the more liberal partial stable model or preferred extension semantics. We study the relationships between proof procedures for different semantics, and argue that, in many meaningful cases, the (simpler) proof procedures for reasoning under the preferred extension semantics can be used as sound and complete procedures for reasoning under the stable model semantics. In many meaningful cases still, proof procedures for credulous reasoning under the preferred extension semantics can be used as (much simpler) sound and complete procedures for sceptical reasoning under the preferred extension semantics. We compare the proposed proof procedures with existing proof procedures in the literature.