Sampler Programs: The Stable Model Semantics of Abstract Constraint Programs Revisited

Abstract

Abstract constraint atoms provide a general framework for the study of aggregates utilized in answer set programming. Such primitives suitably increase the expressive power of rules and enable more concise representation of various domains as answer set programs. However, it is non-trivial to generalize the stable model semantics for programs involving arbitrary abstract constraint atoms. For instance, a nondeterministic variant of the immediate consequence operator is needed, or the definition of stable models cannot be stated directly using primitives of logic programs. In this paper, we propose sampler programs as a relaxation of abstract constraint programs that better lend themselves to the program transformation involved in the definition of stable models. Consequently, the declarative nature of stable models can be restored for sampler programs and abstract constraint programs are also covered if decomposed into sampler programs. Moreover, we study the relationships of the classes of programs involved and provide a characterization in terms of abstract but essentially deterministic computations. This result indicates that all nondeterminism related with abstract constraint atoms can be resolved at the level of program reduct when sampler programs are used as the intermediate representation.