Abstract

As all computational programs, derivation sequences of functional dependences are twice partially ordered sets: by following the instructions in the program and by their execution in time. Order consistency is achieved by the theoretical multiple embedding of one into another. Hereinafter, such sets are referred to as cascade ordered, and there is no need to resort to the terminology of the relational database theory for them. It is possible to represent the derivation sequence in the form of a special union of almost disjoint simple subsequences referred to as pointed sets here. It is achieved by applying a gluing operation \(\ae \) to them. The process of forming a cascade-ordered set of pointed sets is reflected in the title by the term Synthesis. This paper is aimed at studying this process. The final section of the paper sets forth the principles of Analysis, i.e., decomposition of a specified cascade-ordered set into so-called AR cones. This issue will be completely resolved in subsequent papers. Here, logic schemes that are designed to calculate predicates from the given ones are applied for proofs. Flowcharts that are common to algorithmization are less frequently used. Their combined application serves the purposes of automating mathematical proofs. The logical toolkit of the paper is a prerequisite for constructing a mathematical model of artificial intelligence.

中文翻译：

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表功能依赖性推导序列的综合分析

摘要

与所有计算程序一样，功能相关性的派生序列是两次部分排序的集：通过遵循程序中的指令并及时执行它们。顺序一致性是通过理论上将多个对象彼此嵌入在一起来实现的。在下文中，这样的集合被称为级联排序，并且不需要为它们求助于关系数据库理论的术语。可以用几乎不相交的简单子序列的特殊联合形式表示派生序列，在此称为尖集。这是通过对他们应用粘合操作\（\ ae \）来实现的。在标题中，术语“综合”反映了形成一组有序集的尖集的过程。。本文旨在研究此过程。本文的最后一部分阐述了分析的原理，即将指定的级联集分解为所谓的AR锥。此问题将在后续论文中得到完全解决。在这里，设计用于从给定谓词计算谓词的逻辑方案用于证明。算法通用的流程图较少使用。它们的组合应用程序可实现自动化数学证明的目的。本文的逻辑工具包是构建人工智能数学模型的先决条件。