2016
DOI: 10.1017/s1471068416000387
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Stable-unstable semantics: Beyond NP with normal logic programs

Abstract: Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic programs offers the most prominent way of reaching the second level of the PH, but encoding respective hard problems as disjunctive programs typically requires sophisticated techniques such as saturation or meta-interpretation. The application of such techniques easily leads to en… Show more

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Cited by 17 publications
(11 citation statements)
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References 32 publications
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“…A related aspect concerns modeling itself, the process of mapping natural language specifications to formal expressions, which surfaces when one considers problems that require more than one quantifier alternation. It is important to note that combined logic programs were extended to deal with problems from any level of the PH in (Bogaerts et al 2016) by resorting to a recursive definition. This definition forces the programmer to think in terms of "nested oracles", instead of translating problem description directly into a formal expression.…”
Section: Related Work and Discussionmentioning
confidence: 99%
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“…A related aspect concerns modeling itself, the process of mapping natural language specifications to formal expressions, which surfaces when one considers problems that require more than one quantifier alternation. It is important to note that combined logic programs were extended to deal with problems from any level of the PH in (Bogaerts et al 2016) by resorting to a recursive definition. This definition forces the programmer to think in terms of "nested oracles", instead of translating problem description directly into a formal expression.…”
Section: Related Work and Discussionmentioning
confidence: 99%
“…A trivial consequence of Theorem 2 is that this limitation is absent from ASP(Q). Finally, we note that combined programs under stable-unstable semantics have been implemented in a proof of concept prototype (Bogaerts et al 2016) that can only handle problems at the second level of the polynomial hierarchy. A similar prototype implementation for ASP(Q) (programs with at most two quantifiers) is possible, too.…”
Section: Propositionmentioning
confidence: 99%
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“…The framework of stable-unstable semantics by Bogaerts et al [8] provides a similar "guess and check" strategy for solving problems in Σ p 2 . They point out that an advantage of the stable-unstable semantics is they can be easily extended to represent problems at any level of the polynomial hierarchy.…”
Section: Related Encoding Approachesmentioning
confidence: 99%
“…Particularly the hardest problems in this class, the so-called NP-complete problems, suit search based computational approaches, such as ASP, since they currently elude computationally lighter solutions running in deterministic polynomial time. Additionally, ASP provides solutions to problems of even higher complexity in the polynomial-time hierar-Introduction chy [91]: problems in Δ P 2 via optimization [104], problems in Σ P 2 via disjunctive logic programming [42], problems in Δ P 3 via optimization of disjunctive logic programs [78], and problems on arbitrary levels of the hierarchy via so-called stable-unstable semantics [24].…”
Section: Introductionmentioning
confidence: 99%