The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Proceedings of the eleventh international conference on Logic programming
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Contributions to the stable model semantics of logic programs with negation
Theoretical Computer Science
Graph theoretical structures in logic programs and default theories
Theoretical Computer Science
Proceedings of the 1999 international conference on Logic programming
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
On the equivalence and range of applicability of graph-based representations of logic programs
Information Processing Letters
Experiments in Answer Sets Planning
MICAI '00 Proceedings of the Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
Encoding Planning Problems in Nonmonotonic Logic Programs
ECP '97 Proceedings of the 4th European Conference on Planning: Recent Advances in AI Planning
Diagnostic reasoning with A-Prolog
Theory and Practice of Logic Programming
Theory and Practice of Logic Programming
Normal forms for answer sets programming
Theory and Practice of Logic Programming
Graph theoretical characterization and computation of answer sets
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
A Classification Theory Of Semantics Of Normal Logic Programs: I. Strong Properties
Fundamenta Informaticae
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
On the equivalence and range of applicability of graph-based representations of logic programs
Information Processing Letters
P-stable models of strong kernel programs
Journal of Algorithms
Decomposition of declarative knowledge bases with external functions
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Knowledge representation and non-monotonic reasoning
A 25-year perspective on logic programming
A 25-year perspective on logic programming
Answer set modules for logical agents
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
Conflict, consistency and truth-dependencies in graph representations of answer set logic programs
GKR'11 Proceedings of the Second international conference on Graph Structures for Knowledge Representation and Reasoning
A selective semantics for logic programs with preferences
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
Hi-index | 0.00 |
In this paper we analyze the relationship between cyclic definitions and consistency in Gelfond-Lifschitz's answer sets semantics (originally defined as ‘stable model semantics’). This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is given a syntactic characterization. This condition may have a practical importance both for defining new algorithms for checking consistency and computing answer sets, and for improving the existing systems. The approach of this paper is to introduce a new canonical form (to which any logic program can be reduced to), to focus the attention on cyclic dependencies. The technical result is then given in terms of programs in canonical form (canonical programs), without loss of generality: the stable models of any general logic program coincide (up to the language) to those of the corresponding canonical program. The result is based on identifying the cycles contained in the program, showing that stable models of the overall program are composed of stable models of suitable sub-programs, corresponding to the cycles, and on defining the Cycle Graph. Each vertex of this graph corresponds to one cycle, and each edge corresponds to one handle, which is a literal containing an atom that, occurring in both cycles, actually determines a connection between them. In fact, the truth value of the handle in the cycle where it appears as the head of a rule, influences the truth value of the atoms of the cycle(s) where it occurs in the body. We can therefore introduce the concept of a handle path, connecting different cycles. Cycles can be even, if they consist of an even number of rules, or vice versa they can be odd. Problems for consistency, as it is well-known, originate in the odd cycles. If for every odd cycle we can find a handle path with certain properties, then the existence of stable model is guaranteed. We will show that based on this results new classes of consistent programs can be defined, and that cycles and cycle graphs can be generalized to components and component graphs.