Pointwise Logic on Completely Distributive Lattices and Approximate Reasoning

In this paper, we propose the basic framework of point- wise topological logic on completely distributive lattices and explore approximate reasoning in it. The logic of this paper is based on pointwise characterization, therefore the pointwise conception is pervasive. We explore approximate reasoning in abstract logical framework Fl on completely distributive lattice L. We propose the structure of point- wise topological logic F_TL, the structure of matching function sigma. and the structure of matching neighborhood group. We investigate approximate reasoning in pointwise topological logic F_TL with matching function sigma, develop pointwise topological algorithm of simple approximate reasoning, introduce the essential characteristics of this scheme.