2-ASP(Q) programs with weak constraints: Complexity and efficient implementation

We explore the use of answer set programming (ASP) and its extension with quantifiers, ASP(Q), for inconsistency-tolerant querying of prioritized data, where a priority relation between conflicting facts is exploited to define three notions of optimal repairs (Pareto-, globally- and completion-optimal). We consider the variants of three well-known semantics (AR, brave and IAR) that use these optimal repairs, and for which query answering is in the first or second level of the polynomial hierarchy for a large class of logical theories. Notably, this paper presents the first implementation of globally-optimal repair-based semantics, as well as the first implementation of the grounded semantics, which is a tractable under-approximation of all these optimal repair-based semantics. Our experimental evaluation sheds light on the feasibility of computing answers under globally-optimal repair semantics and the impact of adopting different semantics, approximations, and encodings.

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.

Streamliner constraints reduce the search space of combinatorial problems by ruling out portions of the solution space. We adapt the StreamLLM approach, which uses Large Language Models (LLMs) to generate streamliners for Constraint Programming, to Answer Set Programming (ASP). Given an ASP encoding and a few small training instances, we prompt multiple LLMs to propose candidate constraints. Candidates that cause syntax errors, render satisfiable instances unsatisfiable, or degrade performance on all training instances are discarded. The surviving streamliners are evaluated together with the original encoding, and we report results for a virtual best encoding (VBE) that, for each instance, selects the fastest among the original encoding and its streamlined variants. On three ASP Competition benchmarks (Partner Units Problem, Sokoban, Towers of Hanoi), the VBE achieves speedups of up to 4--5x over the original encoding. Different LLMs produce semantically diverse constraints, not mere syntactic variations, indicating that the approach captures genuine problem structure.