Beyond NP: Quantifying over Answer Sets. Issue 5 (September 2019)

• Record Type: Journal Article
• Authors: AMENDOLA, GIOVANNI; RICCA, FRANCESCO; TRUSZCZYNSKI, MIROSLAW
• Is Part Of: Theory and practice of logic programming. Volume 19:Issue 5/6(2019)
• Page Start: 705
• Page End: 721
• Publication Date: 2019-09
• Subjects: ASP, -- Quantified Logics, -- Polynomial Hierarchy; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068419000140
• Languages: English
• ISSNs: 1471-0684

Abstract

Abstract: 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.