SIAM Journal on Computing
Towards automatic autoepistemic reasoning
JELIA '90 Proceedings of the European workshop on Logics in AI
Journal of the ACM (JACM)
Hard problems for simple default logics
Artificial Intelligence - Special issue on knowledge representation
Tractable default reasoning
Relating disjunctive logic programs to default theories
Proceedings of the second international workshop on Logic programming and non-monotonic reasoning
Translating default logic into standard autoepistemic logic
Journal of the ACM (JACM)
The complexity of default reasoning under the stationary fixed point semantics
Information and Computation
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Model Checking for Nonmonotonic Logics: Algorithms and Complexity
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Complexity and Expressive Power of Logic Programming
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
The comparative linguistics of knowledge representation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
The complexity of model checking for belief revision and update
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
The complexity of model checking for propositional default logics
Data & Knowledge Engineering
On the complexity of extension checking in default logic
Information Processing Letters
On the complexity of extension checking in default logic
Information Processing Letters
| Hi-index | 5.23 |
Liberatore and Schaerf (Proceedings of the ECAI' 98, 1998) give a proof that model checking for propositional normal default theories is in Δ2P and Δ2P[O(log n)]-hard. However, the precise complexity is left as an open problem. We solve this problem by proving that model checking for normal default theories is complete for Δ2P[O(log n)]. This is the class of decision problems solvable in polynomial time with a logarithmic number of calls to an oracle in NP. Additionally, we analyse the computational cost of model checking w.r.t, weak extensions, stable expansions and N-expansions and take a look at the complexity of model checking for disjunction-free default theories. Furthermore, we show that not only for disjunction-free default theories, but also for a larger class of default theories, which we call default theories in extended Horn normal form, the complexity of model checking is, in the case of normal default theories, tractable. Additionally, the complexity results are used to draw some interesting conclusions on translatability issues. In particular, there exists no function from default logic into logic programming which is polynomial, faithful and modular unless coNP = Σ2P. Finally, we give an overview of our results concerning model checking in case of disjunctive default logic and stationary default logic.