Beyond NP: Quantifying over Answer Sets
This provides a more elegant and direct way to model complex problems beyond NP in ASP, which is incremental as it extends an existing paradigm.
The authors tackled the limitation of Answer Set Programming (ASP) in modeling problems beyond NP by proposing ASP with Quantifiers (ASP(Q)), an extension that introduces quantifiers over stable models, enabling direct modeling of problems in the Polynomial Hierarchy with natural encodings for applications in AI and number theory.
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 Σ^P_2 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. Under consideration for acceptance in TPLP.