Logic of Knowledge Discovery

在我们的项目项目中，我们研究了知识发现的逻辑基础和知识发现的计算模型。在我们对知识发现的逻辑基础的研究中，我们旨在从哲学和数学逻辑的两个方面给出这种基础，我们研究了“发现的背景”，特别是那些不能简化为逻辑算法的发现。此外，我们还从数学逻辑和形式逻辑的角度研究了发现逻辑的演绎方面。从哲学的角度分析了在发现过程中获取知识和概念的过程，并基于信念修正理论将其形式化。此外，我们还研究了数学中理想概念的引入与数学发现之间的关系，为研究新概念的发现奠定了基础。在知识发现计算模型的研究中，我们研究了与知识发现逻辑相对应的计算模型，并实现了几个实现相应计算模型的系统。特别地，我们在(I)求解分布式匹配空间问题的计算模型，（ii）通过模型检查方法发现算法，以及（iii）从经典逻辑的证明中发现算法的过程中获得了结果。

In our project project, we studied foundations of the logic of knowledge discovery and computation models of knowledge discovery.In our study of foundations of the logic of knowledge discovery, we aimed to give such foundations from the two sides of logic in philosophy and mathematical logic, and we studied the 'context of discovery', in particular, discoveries which cannot be reduced to logical algorithms. Furthermore, we stuidied deductive aspects of logic of discovery from the standpoint of mathematcial and formal loigc. Also, we analyzed the process of acquiring knolwedge and concepts in disccovery from the philosophical standpoint, and we formalized it base on a theory of belief revsion. Moreover, we studied the relationship between the introduction of ideal concepts in mathematics and discovery in mathematcis, and we gave foudations for the study of discovery of new concepts.In our study on computaion models of konwledge discovery, we studied computaion models corresponding to logic of knowledge discovery, and implemented several systems which realize appropriate computation models. In pariticular, we obtained results in (I) a computation model for solving problems in distributed compatation space, (ii) discovery of algorithms by model checking method and (iii) algorithm discovery porcedure from proofs in classical logic.