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INFORMATION MATHEMATICS

信息数学

基本信息

批准号：
07640278
负责人：
KANO Mikio
金额：
$ 1.34万
依托单位：
IBARAKI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

We studied graph theory including genetic algorithms and mathematical logic.For example, we searched (1, f) -odd subgraphs, which are natural generalization of matchings of graphs, and showed that these subgraphs have similar properties as matchings. We also studied connected factors and so on. Furthermore, we considered a problem of straight-line embedding of a graph onto a given set of points in the plane, and obtained some new results. Note that this area was developed in the 1990's, and there are a lot of problems.Some students of our laboratory wrote programs of finding a nearly optimal solutions to some discrete problems by making use of genetic algorithms, and by these test, we can say that genetic algorithms are useful for these problems. However it seems still to be very difficult to analyze theoretically genetic algorithm.The results in mathematical logic are the following. If we take Kripke sheaves as our basic Kripke-type semantics, we can regard the truth-value functor as a presheaf whose codomain is a category of Heyting algebras. This point of view enables us to have a good insight into the structures our subjects. We tried to investigate semantical structures. At first, we introduced categorical concepts and structural properties, and considered correspondences between the truth-value functors and the usual ones. Next, we tried to recognize category-theoretic natural transformations and functors from the stand point of Kripke-sheaf semantics with truth-value functor, and had some fundamental results. *From these results, we have that category-theoretic natural transformations almost correspond to semantical concept called p-morphisms. This observation provides us some natural results. By making use of these results, we studied modal logics, non-classical predicate logics, mainly intermediate predicate logics.

我们学习了图论，包括遗传算法和数理逻辑。例如，我们搜索了(1,f) -奇数子图，这是图的匹配的自然泛化，并证明了这些子图具有与匹配相似的性质。我们还研究了关联因素等。在此基础上，研究了平面上给定点的直线嵌入问题，得到了一些新的结果。请注意，这个地区是在20世纪90年代开发的，存在很多问题。我们实验室的一些学生写了一些程序，利用遗传算法来寻找一些离散问题的近最优解，通过这些测试，我们可以说遗传算法对这些问题很有用。然而，对遗传算法进行理论分析似乎仍然非常困难。数学逻辑的结果如下。如果我们把Kripke束作为我们的基本Kripke型语义，我们可以把真值函子看作一个上域是Heyting代数范畴的预束。这种观点使我们能够很好地洞察我们主题的结构。我们试图研究语义结构。首先，我们引入了范畴概念和结构性质，并考虑了真值函子与一般函子之间的对应关系。其次，我们尝试从Kripke-sheaf语义的角度用真值函子来识别范畴论的自然变换和函子，并得到了一些基本的结果。从这些结果中，我们得到范畴论的自然变换几乎对应于称为p-态射的语义概念。这一观察为我们提供了一些自然的结果。利用这些结果，我们研究了模态逻辑、非经典谓词逻辑，主要是中间谓词逻辑。