Date: 23 Apr 2002

Encodings for Equilibrium Logic and Logic Programs with Nested Expressions

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Equilibrium logic is an approach to nonmonotonic reasoning that generalises the stable model and answer set semantics for logic programs. We present a method to implement equilibrium logic and, as a special case, stable models for logic programs with nested expressions, based on polynomial reductions to quantified Boolean formulas (QBFs). Since there now exist efficient QBF-solvers, this reduction technique yields a practically relevant approach to rapid prototyping. The reductions for logic programs with nested expressions generalise previous results presented for other types of logic programs. We use these reductions to derive complexity results for the systems in question. In particular, we show that deciding whether a program with nested expressions has a stable model is Σ in2 sup complete.

This work was partially supported by the Austrian Science Fund Project under grant P15068.