Finding the stable models of a knowledge base is a significant computational problem in artificial intelligence. This task is at the computational heart of truth maintenance systems, autoepistemic logic, and default logic. Unfortunately, it is NP-hard. In this paper we present a hierarchy of classes of knowledge bases,\Omega 1
|
1177
|
A logic for default reasoning
– Reiter
- 1979
|
|
1126
|
The Stable Model Semantics for Logic Programming
– Gelfond, Lifschitz
- 1988
|
|
557
|
Towards a theory of Declarative Knowledge
– Apt, Blair, et al.
- 1988
|
|
554
|
Classical negation in logic programs and disjunctive databases. New Generation Computing 9:365–385
– Gelfond, Lifschitz
- 1991
|
|
534
|
A truth maintenance system
– Doyle
- 1979
|
|
398
|
Semantical considerations on non-monotonic logic
– Moore
- 1985
|
|
197
|
Foundations of logic programming
– Lifschitz
- 1996
|
|
182
|
Autoepistemic logic
– Marek, Truszczynski
- 1991
|
|
154
|
Nonmonotonic Logic Context-Dependent Reasoning
– Marek, Truszczyński
- 1993
|
|
133
|
Propositional Semantics for Disjunctive Logic Programs
– Ben-Eliyahu, Dechter
- 1994
|
|
125
|
Stable models and non-determinism in logic programs with negation
– Sacc`a, Zaniolo
- 1990
|
|
104
|
On Stratified Autoepistemic Theories
– Gelfond
- 1987
|
|
55
|
Semantic issues in deductive databases and logic programs
– Przymusinska
- 1990
|
|
53
|
Mixed integer programming methods for computing nonmonotonic deductive databases
– Bell, Nerode, et al.
- 1994
|
|
38
|
Minimalism subsumes default logic and circumscription in stratified logic programming
– Bidoit, Froidevaux
- 1986
|
|
36
|
Abduction compared with negation by failure
– Eshgi, Kowalski
- 1989
|
|
35
|
Negation as hypothesis: An abductive foundation for logic programming
– Dung
- 1991
|
|
35
|
Wfs + branch and bound = stable models
– Subrahmanian, Nau
- 1992
|
|
32
|
Hard problems for Simple Default Logics
– Kautz, Selman
- 1991
|
|
32
|
Computing abduction using the TMS
– Satoh, Iwayama
- 1991
|
|
29
|
Stable theories for logic programs
– Kakas, Mancarella
- 1991
|
|
27
|
Computing the extensions of autoepistemic and default logics with a truth maintenance system
– Junker, Konolige
- 1990
|
|
21
|
Default reasoning using classical logic
– Ben-Eliyahu, Dechter
- 1996
|
|
20
|
Reasoning with stratified default theories
– Cholewi'nski
- 1995
|
|
15
|
Stratified default theories
– Cholewi'nski
- 1995
|
|
13
|
Structure-driven algorithms for truth maintenance
– Dechter, Dechter
- 1996
|
|
11
|
A graph-theoretic approach to default logic
– Dimopoulos, Magirou
- 1994
|
|
11
|
The justification of negation as failure
– Fine
- 1989
|
|
11
|
Effective implementation of negation in database logic query languages
– Leone, Romeo, et al.
- 1993
|
|
5
|
A truth maintenance system based on stable models
– Pimentel
- 1989
|
|
4
|
Soundness and completeness of a logic programming approach to default logic
– Antoniou
- 1994
|
|
4
|
A Hierarchy of Tractable Subsets
– Elkan
- 1990
|
|
3
|
Polynomial-time computable stable models.. Annals of Mathematics and
– Palopoli
- 1996
|
|
