Abstract To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration amongst these, contemporary representation methodologies offer little support for this. In an attempt to alleviate this situation, we position and motivate a new declarative programming framework in this paper. We focus on the semantical foundations in service of providing abstractions of well-known problems such as SAT, Bayesian inference, generative models, learning and convex optimization. Programs are understood in terms of first-order logic structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines and represent non-standard problems over unbounded domains. Thus, the main thrust of this paper is to view such well-known problems through a unified lens in the hope that appropriate solver strategies (exact, approximate, portfolio or hybrid) may emerge that tackle real-world problems in a principled way.

中文翻译：

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半环规划：广义和积问题的语义框架

摘要 为了解决难题，人工智能依赖于多种学科，如逻辑、概率推理、机器学习和数学编程。尽管人们普遍认为解决现实世界的问题需要在这些问题之间进行整合，但当代表示方法对此几乎没有提供支持。为了缓解这种情况，我们在本文中定位并激发了一个新的声明式编程框架。我们专注于提供对 SAT、贝叶斯推理、生成模型、学习和凸优化等众所周知问题的抽象服务的语义基础。程序被理解为带有半环标签的一阶逻辑结构，这使我们能够自由地组合和整合来自不同 AI 学科的问题，并在无界域上表示非标准问题。因此，本文的主要目的是通过统一的视角来看待这些众所周知的问题，希望能出现合适的求解器策略（精确、近似、组合或混合），以有原则的方式解决现实世界的问题。