Using ASP(Q) to Handle Inconsistent Prioritized Data

In this paper, we explore the issue of inconsistency handling over prioritized knowledge bases (KBs), which consist of an ontology, a set of facts, and a priority relation between conflicting facts. In the database setting, a closely related scenario has been studied and led to the definition of three different notions of optimal repairs (global, Pareto, and completion) of a prioritized inconsistent database. After transferring the notions of globally-, Pareto- and completion-optimal repairs to our setting, we study the data complexity of the core reasoning tasks: query entailment under inconsistency-tolerant semantics based upon optimal repairs, existence of a unique optimal repair, and enumeration of all optimal repairs. Our results provide a nearly complete picture of the data complexity of these tasks for ontologies formulated in common DL-Lite dialects. The second contribution of our work is to clarify the relationship between optimal repairs and different notions of extensions for (set-based) argumentation frameworks. Among our results, we show that Pareto-optimal repairs correspond precisely to stable extensions (and often also to preferred extensions), and we propose a novel semantics for prioritized KBs which is inspired by grounded extensions and enjoys favourable computational properties. Our study also yields some results of independent interest concerning preference-based argumentation frameworks.

ASP(Q) extends Answer Set Programming (ASP) with Quantifiers over answer sets. In this paper we focus on the class of ASP(Q) programs with two quantifiers and weak constraints, denoted as 2-ASP(Q)^w. 2-ASP(Q)^w is a practically relevant fragment of ASP(Q) that is expressive enough to capture optimization problems up to the class Delta_3^P. On the theoretical side, we provide a complete complexity characterization of the main computational tasks for 2-ASP(Q)^w programs, including tight completeness results and the analysis of nontrivial cases that have not been addressed in previous works. On the practical side, we introduce novel strategies for computing (optimal) quantified answer sets in the Casper system, that rely on a Counterexample-Guided Abstraction Refinement (CEGAR) technique tailored to ASP(Q). An experimental evaluation on hard benchmarks from different application domains shows that the proposed techniques are effective in practice.

Writing Answer Set Programming (ASP) theories from scratch is a difficult and time-consuming task. We take a neurosymbolic approach to study whether a model can distill complete and correct theories, given a fixed agent harness with the solver in the loop. The protocol is dataset-agnostic: with a single prompt and an empty file as the starting point the model is given a 1-hour time limit to derive a complete theory. We chose VQA as the application domain, three benchmarks (CLEVR, GQA, CLEVRER), as these are publicly available and non-trivial. In order to study the model scale required for solving this task we nine different models: four frontier (Claude Sonnet 4.6, Claude Opus 4.7, GPT-5, DeepSeek V4 Pro), two mid-tier (DeepSeek V4 Flash, gpt-oss-120b), and three open-weights (qwen3.6-27b, gpt-oss-20b, qwen3.5-9b). Three of four frontier models reach 100% on CLEVR and 92.8%-98.8% on GQA; on CLEVRER, Sonnet, Opus, DeepSeek V4 Pro score 92.7%-95.3%. GPT-5 reaches 98.7% on CLEVR but drops to 41.8% on GQA and to 86.7% on CLEVRER. Adding handwritten reference theories from other datasets moves the other three frontier models by at most +/-3.4 pp but reduces GPT-5's accuracy by 3-19 pp. We release the code, prompts, and theories distilled.