Semantical considerations on nonmonotonic logic
Artificial Intelligence
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Extended stable semantics for normal and disjunctive programs
Logic programming
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Default theories of Poole-type and a method for constructing cumulative versions of default logic
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
A three-valued semantics for deductive databases and logic programs
Journal of Computer and System Sciences
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
Querying disjunctive databases through nonmonotonic logics
Theoretical Computer Science
Unfounded sets and well-founded semantics for general logic programs
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Artificial Intelligence
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
Nested expressions in logic programs
Annals of Mathematics and Artificial Intelligence
On the intertranslatability of non-monotonic logics
Annals of Mathematics and Artificial Intelligence
Separating Disbeliefs from Beliefs in Autoepistemic Reasoning
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Classifying Semi-Normal Default Logic on the Basis of its Expressive Power
LPNMR '99 Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning
On the Effect of Default Negation on the Expressiveness of Disjunctive Rules
LPNMR '01 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
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Janhunen et al. [14] have proposed a translation technique for normal logic programs in order to capture the alternating fix-points of a program with the stable models of the translation. The same technique is also applicable in the disjunctive case so that partial stable models can be captured. In this paper, the aim is to capture Przymusinska and Przymusinski's stationary extensions with Reiter's extensions using the same translational idea. The resulting translation function is polynomial, but only weakly modular and not perfectly faithful. Fortunately, another technique leads to a polynomial, faithful and modular (PFM) translation function. As a result, stationary default logic (STDL) is ranked in the expressive power hierarchy (EPH) of non-monotonic logics [13]. Moreover, reasoning with stationary extensions as well as brave reasoning with regular extensions (i.e., maximal stationary extensions) can be implemented using an inference engine for reasoning with Reiter's extensions.