Knowledge Mass and Multiple Approximate Reasoning in Type I Topological Logic C1 T

In this paper, we propose and investigate the type I knowledge mass, type I knowledge base, type I approximate knowledge closure of knowledge base, type I topological algorithm of multiple approximate reasoning in the framework of type I topological logic C¹ _T. For the type I topological algorithm of multiple approximate reasoning, Frechet topology is also a critical topology. It is only valid for the the multiple approximate reasonings with A* isin {A_i | i = 1, 2,... , n}, and is invalid for the multiple approximate reasonings which allow A* isin F(S) - {Ai | i = 1, 2, ... ,n}. The topologies which are valid for the type I topological algorithm of the multiple approximate reasoning , can only be the non-Frechet topologies. These topologies can realize not only the classic MP reasoning but also the non-classic approximate reasoning. It can activate some knowledge Ai rarr Bi as A* isin F(S) - {A_i | i = 1,2,... ,n}.