A MaxSAT-based Framework for Computing Circumscription

The circumscription is an elegant non-monotonic logic. However, computing circumscription remains challenging due to its computational complexity. This paper presents a weighted partial Maximum Satisfiability (MaxSAT) encoding approach that addresses circumscription, allowing us to leverage state-of-the-art MaxSAT solvers for efficient computation. This approach introduces a linear-time encoding scheme that captures both parallel and prioritized circumscription without requiring fresh predicates. Furthermore, we develop a systematic model enumeration strategy using blocking clauses, which enables the complete and efficient enumeration of circumscription models while avoiding redundancy. Extensive experiments have been conducted on benchmarks such as model-based circuit diagnostics, random and industrial SAT problems, and extended stable marriage problems. The results indicate that our MaxSAT-based implementation, circ-maxsat, achieves comparable performance with state-of-the-art methods such as circ2dlp and aspino. Notably, circ-maxsat outperforms other solvers on the (extended) stable marriage problem in terms of computational efficiency. This study advances the computation of circumscription and introduces new applications of MaxSAT in non-monotonic reasoning.