|Budget Amount *help
¥2,100,000 (Direct Cost : ¥2,100,000)
Fiscal Year 1996 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1995 : ¥1,400,000 (Direct Cost : ¥1,400,000)
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.