DIGITAL COMPUTATIONAL METHODS IN SYMBOLIC LOGIC, WITH EXAMPLES IN BIOCHEMISTRY.
DIGITAL COMPUTATIONAL METHODS IN SYMBOLIC LOGIC, WITH EXAMPLES IN BIOCHEMISTRY.
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DOI：
10.1073/pnas.41.7.498
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发表时间：
1955-07
影响因子：
11.1
通讯作者：
Robert S. Ledley
中科院分区：
文献类型：
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作者：
Robert S. Ledley
符号逻辑的形式理论，在1900年之前由布尔、皮尔斯、杰文斯、施罗德和其他学者发展，在世纪之交之后由怀特海、罗素、希尔伯特、哥德尔等人发展，它作为科学方法和思想的基石，其基础性的重要性得到了普遍的认可。然而，它在很大程度上仍然是一个哲学和深奥的研究领域，并且还没有实际的直接计算方法来直接大规模应用于特定类型的现实问题。本文的目的不是在符号逻辑的形式理论中提出任何新的结果，而是在命题演算中提供一种新的数字化计算方法系统，用于解决科学、工业和政府中经常出现的大量实际非数值问题。其目的是形成一种极其简单的逻辑“算术”，它将为非数值问题领域提供系统的解决方法，就像数值分析解决数值性质的问题那样简单、直接和通用。布尔方程理论成为本文所提出的更一般方法的一个特殊实例。人们可能没有意识到，符号逻辑和相关的布尔代数（集合和类的微积分）的方法可以攻击和解决多么广泛的问题。逻辑的直接应用总是有助于演绎推理，比如确定给定前提、规则或公理的结果，并提出假设或定理，从这些假设或定理中可以推导出给定的前提或事实关系。除了在与句子有关的问题中使用逻辑命题方法，例如对军事情报报告和法律和保险文件的分析，在运运学、生物学、医学、实验设计等领域似乎还有更重要的应用，在这些领域，符号逻辑本身的效用并不是那么明显。现在符号逻辑的命题演算的结果是
The formal theory of symbolic logic, as developed by Boole,'Peirce, 2 Jevons, 3 and Schrdder4 before 1900 and by Whitehead, Russell, Hilbert, G6del, and others after the turn of the century, is universally recognized for its fundamental im-portance as a cornerstone of scientific method and thought. Yet it has remained largely a philosophic and esoteric realm of study, and there have existed no methods of actual straightforward computation for direct large-scale applications to specific types of realistic problems. The purpose of this paper is not to present any new results in the formal theory of symbolic logic, but rather to offer a new system of digitalized computational methods in the propositional calculus for application to the great number of practical nonnumerical problems that so frequently occur in science, industry, andgovernment. The object was to formulate a logical" arithmetic" of extreme simplicity, which would provide, for this realm of non-numerical problems, systematic methods of solution as simple, straightforward, and versatile as those ofnumerical analysis are for problems ofa numerical nature. The theory of Boolean equations becomes a special instance of the more general methods presented in this paper.It is perhaps not generally realized how wide a range of problems can be attacked and solved by methods of symbolic logic and the related Boolean algebra, which is the calculus of sets and classes. Direct application of logic can always be an aid to deductive reasoning-such as determining consequences of given premises, rules, or axioms and making hypotheses or theorems from which the given premises or factual relationships can be deduced. Besides the use of logical propositional methods in problems concerned with sentences, such as analysis of military in-formation reports and legal and insurance documents, there appear to be even more important applications to fields of operations research, biology, medicine, design of experiments, etc., where the utility of symbolic logic per se is not-as immediately evident. Now that the results of the propositional calculus of symbolic-logic are