This paper extends these results in several directions. First, the syntactic features of programs, viz. cyclic negative dependencies, affecting the existence of stable models are characterized, and their relevance is discussed. Next, a new graph representation of logic programs, the Extended Dependency Graph (EDG), is introduced, which conveys enough information for reasoning about stable models (while the traditional Dependency Graph does not). Finally, we show that the problem of the existence of stable models can be reformulated in terms of coloring of the EDG

Introduction Stable Logic Programming (SLP) (MarTru99), also called Answer Set Programming (ASP) (Lif99), is an emergent, alternative style of logic programming: each solution to a problem is represented by an answer set, and not by answer substitutions produced in response to a query. A main open problem is that of defining programming methodologies for SLP. Up to now, all programs discussed in the literature have a common, simple structure, that guarantees the existence of stable models (or, equivalently, of answer sets) by construction. As soon as SLP will be more widely and practically applied, the need will most likely arise of writing programs with a more complicated structure, and of composing existing programs into larger ones. Guidelines should be provided to programmers and system developers, in order to write consistent programs, and to combine them. Thus, program analysis tools should be made available, so as to define and check properties of programs. These tools m