Weight Constraints as Nested Expressions

TL;DR

This paper demonstrates a translation from weight constraints to nested expressions in logic programming, enabling the use of satisfiability solvers and logical equivalence proofs for programs with weight constraints.

Contribution

It introduces a simple, modular translation from weight constraints to nested expressions, facilitating answer set computation and equivalence analysis.

Findings

Translation preserves answer sets of programs with weight constraints.

Nested expressions can be eliminated in favor of additional atoms.

Enables use of satisfiability solvers for weight constraint programs.

Abstract

We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and Simons, uses weight constraints. We show that there is a simple, modular translation from the language of weight constraints into the language of nested expressions that preserves the program's answer sets. Nested expressions can be eliminated from the result of this translation in favor of additional atoms. The translation makes it possible to compute answer sets for some programs with weight constraints using satisfiability solvers, and to prove the strong equivalence of programs with weight constraints using the logic of here-and there.