| Answer set programming (ASP), namely logic programming under the answer set semantics, provides a promising constraint programming paradigm, due to its simple syntax, high expressiveness, and effective computational properties. This programming paradigm can be viewed as a variant of SAT. A main drawback of ASP, like SAT, is that the framework is primarily formulated for reasoning with individuals, where each is represented by an atom in the traditional sense. Recently, ASP has been extended to include constraints to facilitate reasoning with sets of atoms in an explicit manner. These constraints include weight constraints, aggregates, and abstract constraints. Logic programs with these constraints are referred to as weight constraint, aggregate and abstract constraint programs.;We investigate the properties and computations of weight constraint, aggregate, and abstract constraint programs, respectively. For properties, we improve the formulation of loop formulas for weight constraint and aggregate programs, propose loop formulas for abstract constraint programs, and characterize strong equivalence of these programs. For computations, we refine the existing constraint propagation mechanism in the computation of weight constraint programs and advocate a new approach to computing aggregate programs. |
