Implementing Stable-Unstable Semantics with ASPTOOLS and Clingo

Normal logic programs subject to stable model semantics cover reasoning problems from the first level of polynomial time hierarchy (PH) in a natural way. Disjunctive programs reach one level beyond this, but the access to the underlying NP oracle(s) is somewhat implicit and available for the programmer using the so-called saturation technique. To address this shortcoming, stable-unstable semantics was proposed, making oracles explicit as subprograms having no stable models. If this idea is applied recursively, any level of PH can be reached with normal programs only, in analogy to quantified Boolean formulas (QBFs). However, for the moment, no native implementations of stable-unstable semantics have emerged except via translations toward QBFs. In this work, we alleviate this situation with a translation of (effectively) normal programs that combines a main program with any fixed number of oracles subject to stable-unstable semantics. The result is a disjunctive program that can be fed as input for answer set solvers supporting disjunctive programs. The idea is to hide saturation from the programmer altogether, although it is exploited by the translation internally. The translation of oracles is performed using translators and linkers from the ASPTOOLS collection while Clingo is used as the back-end solver.