Weight Constraint Programs with Functions

In this paper we consider a new class of logic programs, called weight constraint programs with functions, which are lparse programs incorporating functions over non-Herbrand domains. We define answer sets for these programs and develop a computational mechanism based on loop completion. We present our results in two stages. First, we formulate loop formulas for lparse programs (without functions). Our result improves the previous formulations in that our loop formulas do not introduce new propositional variables, nor there is a need of translating lparse programs to nested expressions. Building upon this result we extend the work to weight constraint programs with functions. We show that the loop completion of such a program can be transformed to a Constraint Satisfaction Problem (CSP) whose solutions correspond to the answer sets of the program, hence off-the-shelf CSP solvers can be used for answer set computation. We show some preliminary experimental results.