Beyond NP: Quantifying over Answer Sets

Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling problems beyond NP with ASP is known to be complicated, on the one...

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Bibliographic Details
Published in:Theory and practice of logic programming Vol. 19; no. 5-6; pp. 705 - 721
Main Authors: AMENDOLA, GIOVANNI, RICCA, FRANCESCO, TRUSZCZYNSKI, MIROSLAW
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.09.2019
Subjects:
35th International Conference on Logic Programming
Artificial intelligence
Boolean algebra
Declarative programming
Logic programming
Mathematical programming
Number theory
Original Article
Polynomials
Quantified Logics
Polynomial Hierarchy
ASP
ISSN:1471-0684, 1475-3081
Online Access:Get full text
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Summary:Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling problems beyond NP with ASP is known to be complicated, on the one hand, and limited to problems in $\[\Sigma _2^P\]$ on the other. Inspired by the way Quantified Boolean Formulas extend SAT formulas to model problems beyond NP, we propose an extension of ASP that introduces quantifiers over stable models of programs. We name the new language ASP with Quantifiers (ASP(Q)). In the paper we identify computational properties of ASP(Q); we highlight its modeling capabilities by reporting natural encodings of several complex problems with applications in artificial intelligence and number theory; and we compare ASP(Q) with related languages. Arguably, ASP(Q) allows one to model problems in the Polynomial Hierarchy in a direct way, providing an elegant expansion of ASP beyond the class NP.
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ISSN:1471-0684
1475-3081
DOI:10.1017/S1471068419000140