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Stable-unstable semantics: Beyond NP with normal logic programs

Published online by Cambridge University Press:  14 October 2016

BART BOGAERTS ,
TOMI JANHUNEN  and
SHAHAB TASHARROFI
BART BOGAERTS
Affiliation:
Helsinki Institute for Information Technology HIIT * Department of Computer Science, Aalto University, FI-00076 AALTO, Finland, (e-mail: firstname.lastname@aalto.fi)
TOMI JANHUNEN
Affiliation:
Helsinki Institute for Information Technology HIIT * Department of Computer Science, Aalto University, FI-00076 AALTO, Finland, (e-mail: firstname.lastname@aalto.fi)
SHAHAB TASHARROFI
Affiliation:
Helsinki Institute for Information Technology HIIT * Department of Computer Science, Aalto University, FI-00076 AALTO, Finland, (e-mail: firstname.lastname@aalto.fi)
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Abstract

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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 encodings that are inaccessible to non-experts. Furthermore, while disjunctive ASP solvers often rely on calls to a (co-)NP oracle, it may be difficult to detect from the input program where the oracle is being accessed. In other formalisms, such as Quantified Boolean Formulas (QBFs), the interface to the underlying oracle is more transparent as it is explicitly recorded in the quantifier prefix of a formula. On the other hand, ASP has advantages over QBFs from the modeling perspective. The rich high-level languages such as ASP-Core-2 offer a wide variety of primitives that enable concise and natural encodings of search problems. In this paper, we present a novel logic programming–based modeling paradigm that combines the best features of ASP and QBFs. We develop so-called combined logic programs in which oracles are directly cast as (normal) logic programs themselves. Recursive incarnations of this construction enable logic programming on arbitrarily high levels of the PH. We develop a proof-of-concept implementation for our new paradigm.

Keywords

disjunctive logic programmingpolynomial hierarchyquantified Boolean formulas
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Special Issue 5-6: 32nd International Conference on Logic Programming , September 2016 , pp. 570 - 586
Copyright
Copyright © Cambridge University Press 2016 

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