Logic and logic programming
Logic and logic programming
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逻辑和逻辑编程
DOI：
10.1145/131295.131296
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
J. A. Robinson
中科院分区：
文献类型：
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作者：
J. A. Robinson
Logic已经存在了很长时间[23]。在23个世纪前，即亚里士多德时代（公元前384-322年），它已经是一个古老的主题。虽然亚里士多德不是它的创始人，尽管广泛的印象相反，他肯定是它的第一个重要人物。他把逻辑的健全系统的基础上，这是一个主要的课程研究在他自己的大学在雅典举行。他关于逻辑学的讲义今天仍然可以读到。毫无疑问，他教逻辑未来的亚历山大大帝时，他担任了一段时间的年轻王子的私人导师。一代人之后（大约公元前300年），在亚历山大，欧几里得在系统化和教授那个时代的几何和数论方面发挥了类似的作用。亚里士多德的逻辑学和欧几里得的几何学都经受住了考验，并取得了繁荣。在一些高中和大学，这两种课程仍然以类似于原来的形式教授。然而，旧的逻辑学，就像旧的几何学一样，现在已经发展成一种更普遍和更强大的形式。现代（“符号”或“逻辑”）逻辑可以追溯到1879年，当时弗雷格发表了今天被称为谓词演算的第一个版本。这个系统提供了一个丰富而全面的符号，弗雷格打算用它来表达所有的数学概念，并对它们进行精确的演绎推理。似乎是这样。谓词演算的主要特征是它提供了证明概念的精确表征。它的证明，以及它的句子和它的其他形式表达，是数学定义的对象，不仅是为了有意义地表达思想-也就是说，被用来作为一个使用语言-但也是数学分析的主题。在世纪末，数学已经发展到了一个阶段，它已经准备好利用弗雷格强大的新工具。数学家们正在开辟新的研究领域，这些领域需要比以前更深入的逻辑理解和更仔细的证明。其中一些是大卫希伯特的抽象公理重铸的几何和朱塞佩皮亚诺的算术，以及康托的直觉探索一般集理论，特别是他阐述了令人眼花缭乱的理论超限序数和基数。其他人恩斯特策梅罗的公理分析集理论的发现后，
L ogic has been around for a very long time [23]. It was already an old subject 23 centuries ago, in Aristotle's day (384-322 BC). While Aristotle was not its originator, despite a widespread impression to the contrary, he was certainly its first important figure. He placed logic on sound systematic foundations, and it was a major course of study in his own university in Athens. His lecture notes on logic can still be read today. No doubt he taught logic to the future Alexander the Great when he served for a time as the young prince's personal tutor. In Alexandria a generation later (about 300 BC), Euclid played a similar role in systematizing and teaching the geometry and number theory of that era. Both Aristotle's logic and Euclid's geometry have endured and prospered. In some high schools and colleges, both are still taught in a form similar to their original one. The old logic, however, like the old geometry, has by now evolved into a much more general and powerful form. Modern ('symbolic'or'mathematical') logic dates back to 1879, when Frege published the first version of what today is known as the predicate calculus [14]. This system provides a rich and comprehensive notation, which Frege intended to be adequate for the expression of all mathematical concepts and for the formulation of exact deductive reasoning about them. It seems to be so. The principal feature of the predicate calculus is that it offers a precise characterization of the concept of proof. Its proofs, as well as its sentences and its other formal expressions, are mathematically defined objects which are intended not only to express ideas meaningfully--that is, to be used as one uses a language--but also to be the subject matter of mathematical analysis. They are also capable of being manipulated as the data objects of construction and recognition algorithms.At the end of the nineteenth century, mathematics had reached a stage in which it was more than ready to exploit Frege's powerful new instrument. Mathematicians were opening up new areas of research that demanded much deeper logical understanding and far more careful handling of proofs, than had previously been required. Some of these were David Hiibert's abstract axiomatic recasting of geometry and Giuseppe Peano's of arithmetic, as well as Georg Cantor's intuitive explorations of general set theory, especially his elaboration of the dazzling theory of transfinite ordinal and cardinal numbers. Others were Ernst Zermelo's axiomatic analysis of set theory following the discov-