Probabilistic Reasoning within Answer Set Programming with Quantifiers

Answer Set Programming with Quantifiers (ASP(Q)) extends Answer Set Programming (ASP) by allowing quantification over answer sets. Although probabilistic extensions to ASP exist, there is no such counterpart for ASP(Q). In this paper, we close this gap by introducing Inferential Quantified Answer Set Programming (ASP(Q)Inf), an extension of ASP(Q) that supports probabilistic inference over programs with alternating quantifiers, allowing uncertainty at the innermost level. We demonstrate the modeling capabilities of ASP(Q)Inf, analyze its computational complexity, and present an implementation based on Algebraic Model Counting. An experimental evaluation confirms its effectiveness and practical applicability.