Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational meaning of ordered disjunction is clear, there exists an important open issue regarding its semantics. In particular, there does not exist a purely model-theoretic approach for determining the most preferred models of an LPOD. At present, the selection of the most preferred models is performed using a technique that is not based exclusively on the models of the program and in certain cases produces counterintuitive results. We provide a novel, model-theoretic semantics for LPODs, which uses an additional truth value in order to identify the most preferred models of a program. We demonstrate that the proposed approach overcomes the shortcomings of the traditional semantics of LPODs. Moreover, the new approach can be used to define the semantics of a natural class of logic programs that can have both ordered and classical disjunctions in the heads of clauses. This allows programs that can express not only strict levels of preferences but also alternatives that are equally preferred. This work is under consideration for acceptance in TPLP.
我们扩展答案集语义处理不一致的程序（包含经典否定），通过找到一个“最佳”的答案集。在不一致的程序中，规则的偏序是很自然的，表示满足某些规则的偏好，可能以违反不太重要的规则为代价。我们表明，这样的规则顺序诱导一个自然的顺序扩展的答案集，我们称之为首选答案集的最小元素。我们描述了所得到的语义的表达性，并表明它可以模拟否定失败，析取和其他一些形式主义，如逻辑程序有序析取。该方法被证明是有用的，在几个应用领域，例如修复数据库，其中最小的维修对应于首选的答案集。逻辑程序设计理论与实践（Theory and Practice of Logic Programming，TPLP）
ANDRE: An Attention-based Neuro-symbolic Differentiable Rule Extractor for Inductive Logic Programming
Dept. of Mechanical and Aerospace Engineering, George Washington University, USA（机械与航空航天工程系，乔治华盛顿大学）；Dept. of Mechanical Engineering Sciences, University of Surrey, UK（机械工程科学系，萨里大学）
QMFOL: Benchmarking Large Language Model Reasoning via Quantifiable Monadic First-Order Logic Test Case Generation
Huazhong University of Science and Technology（华中科技大学）；Nanyang Technological University（南洋理工大学）；Hubei University（湖北大学）；East China Normal University（华东师范大学）；National University of Singapore（新加坡国立大学）
