Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs, including in attempting to solve the well-known Russell's paradox. These semantics are often non-intuitive and hard-to-understand when unrestricted negation is used in recursion. This paper describes a simple new semantics for logic rules, founded semantics, and its straightforward extension to another simple new semantics, constraint semantics, that unify the core of different prior semantics. The new semantics support unrestricted negation, as well as unrestricted existential and universal quantifications. They are uniquely expressive and intuitive by allowing assumptions about the predicates, rules, and reasoning to be specified explicitly, as simple and precise binary choices. They are completely declarative and relate cleanly to prior semantics. In addition, founded semantics can be computed in linear time in the size of the ground program.

中文翻译：

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建立逻辑规则的语义和约束语义

逻辑规则和推理是计算机科学的基础，并已被广泛研究。然而，逻辑语言的先验语义可能具有微妙的含义，甚至在非常简单的程序中也可能存在显着分歧，包括试图解决著名的罗素悖论。当在递归中使用不受限制的否定时，这些语义通常不直观且难以理解。本文描述了一个简单的逻辑规则新语义，即已建立的语义，以及它对另一个简单的新语义的直接扩展，约束语义，统一了不同先验语义的核心。新语义支持不受限制的否定，以及不受限制的存在和全称量化。通过允许对谓词、规则、和推理要明确指定，作为简单而精确的二元选择。它们是完全声明性的，并且与先前的语义完全相关。此外，可以根据地面程序的大小在线性时间内计算已建立的语义。