# Quantifying over Optimum Answer Sets

arXiv: https://arxiv.org/abs/2408.07697 · HTML: https://mlsanity.com/paper/2408.07697/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 5 of 5)

- [ASP-Core-2 Input Language Format](https://mlsanity.com/paper/1911.04326/) (2019)
- [Planning with Incomplete Information in Quantified Answer Set Programming](https://mlsanity.com/paper/2108.06405/) (2021)
- [Beyond NP: Quantifying over Answer Sets](https://mlsanity.com/paper/1907.09559/) (2019)
- [Stable-Unstable Semantics: Beyond NP with Normal Logic Programs](https://mlsanity.com/paper/1608.01835/) (2016)
- [Unit Testing in ASP Revisited: Language and Test-Driven Development Environment](https://mlsanity.com/paper/2401.02153/) (2024)

## Built on by (most cited first, 1 of 1)

- [2-ASP(Q) programs with weak constraints: Complexity and efficient implementation](https://mlsanity.com/paper/2605.27338/) (2026)

## Abstract (arXiv)

Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way problems requiring a polynomial number of calls to an oracle in Sigmanp (that is, problems in Deltan+1p). Such problems include, in particular, optimization problems. In this paper we propose an extension of ASP(Q), in which component programs may contain weak constraints. Weak constraints can be used both for expressing local optimization within quantified component programs and for modeling global optimization criteria. We showcase the modeling capabilities of the new formalism through various application scenarios. Further, we study its computational properties obtaining complexity results and unveiling non-obvious characteristics of ASP(Q) programs with weak constraints.