Pointwise Logic on Completely Distributive Lattices and Approximate Reasoning

In this paper, we propose the basic framework of pointwise 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 [or \mathbb{F}_{L}] on completely distributive lattice L. We propose the structure of pointwise topological logic FTL [or \mathbb{F}_{TL}], the structure of matching function \sigma and the structure of matching neighborhood group. We investigate approximate reasoning in pointwise topological logic FTL [or \mathbb{F}_{L}] with matching function σ [or \sigma], develop pointwise topological algorithm of simple approximate reasoning, introduce the essential characteristics of this scheme.