The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Contributions to the stable model semantics of logic programs with negation
Theoretical Computer Science
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
Graphs and colorings for answer set programming
Theory and Practice of Logic Programming
On the existence of stable models of non-stratified logic programs
Theory and Practice of Logic Programming
P-stable models of strong kernel programs
Journal of Algorithms
A 25-year perspective on logic programming
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
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Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the kernel of the program, is useful for studying existence and number of answer sets. A kernel program is composed of the atoms which are undefined in the Well-founded semantics, which are those that directly affect the existence of answer sets. The body of rules is composed of negative literals only. Thus, the kernel form tends to be significantly more compact than other formulations. Also, it is possible to check consistency of kernel programs in terms of colorings of the Extended Dependency Graph program representation which we previously developed. The second normal form is called 3-kernel. A 3-kernel program is composed of the atoms which are undefined in the Well-founded semantics. Rules in 3-kernel programs have at most two conditions, and each rule either belongs to a cycle, or defines a connection between cycles. 3-kernel programs may have positive conditions. The 3-kernel normal form is very useful for the static analysis of program consistency, i.e. the syntactic characterization of existence of answer sets. This result can be obtained thanks to a novel graph-like representation of programs, called Cycle Graph which presented in the companion article Costantini (2004b).