Information Semantics and Relational Programming in Dedekind Categories

本项目对Dedekind范畴中的信息语义和关系编程以及计算机科学中的关系方法进行了四年的研究，主要成果如下：（1）（二元）关系的基数性的基础，包括Dedekind不等式。(2)Tarski不动点定理在Dedekind范畴中的另一种证明。（3）具有三重局部转移规则的经典自动机可逆性的判定。(4)验证恶魔的组成和恶魔之间的订单的意义的程序在戴德金类别。通过该基金的援助，作者可以给讲座的结果，由研究项目，特别是，可以服务于国际会议的程序委员会的关系方法在计算机科学/应用Kleene代数。作者谨向所有支持该科学项目的人表示衷心的感谢。

The project studied on Information Semantics and Relational Programming in Dedekind categories and the relationalmethods in Computer Science for four years and the main results are the following :(1) The foundations of the cardinality of (binary) relations, including Dedekind inequality.(2) Another proof of Tarski's fixed point theorem in Dedekind categories,(3) Determination of the reversibility for classic automata with triplet local transition rules.(4) Verification of demonic composition and demonic orders between meanings of programs in Dedekind categories.By the aid of the fund the author could give lectures on the results by the study project, in particular, could serve a program committee of the International Conference on Relational Methods in Computer Science/Applications of Kleene Algebras. The author would like to express his sincere gratitude for all persons who support the scientific project.