INFORMATION MATHEMATICS

我们研究了包括遗传算法和数学逻辑在内的图论，例如，我们研究了图的匹配的自然推广--(1，f)-奇子图，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。此外，我们还考虑了图在平面上给定点集上的直线嵌入问题，得到了一些新的结果。值得注意的是，这个领域是在90年代的S发展起来的，问题很多。我们实验室的一些学生编写了利用遗传算法来寻找一些离散问题的近最优解的程序，通过这些测试，我们可以说遗传算法在这些问题上是有用的。然而，从理论上分析遗传算法似乎仍然非常困难。数理逻辑的结果如下。如果我们把Kriske层作为我们的基本Krigke型语义，我们可以把真值函子看作是一个预层，它的上域是Heyting代数范畴。这一观点使我们能够很好地洞察我们的主题的结构。我们试图研究语义结构。首先，我们介绍了范畴概念和结构性质，并考虑了真值函子与通常函子之间的对应关系。接下来，我们尝试用真值函子来识别范畴论中的自然变换和函子，并取得了一些基本的结果。*从这些结果中，我们得到范畴理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。

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.