Knowledge Compatibility Representation and Reasoning in Incomplete Formal Contexts from Logical Perspective
The incomplete information in formal contexts leads to the incompatibility of knowledge,that is,implications cannot hold simultaneously in any completion of an incomplete formal context.Logical description is a methodology for representing knowledge from a semantic aspect and establishing inference rules with semantic coordination from a syntactic aspect.This paper firstly studies the compatibility semantic representation within incomplete data from a logical perspective,characterizes the sound-ness and compatibility of knowledge via incomplete instances,and constructs the most compact compatible set(namely compatible canonical basis).Secondly,this paper establishes inference rules with semantic soundness,compatibility,and completeness to avoid incompatible knowledge and invalid knowledge in knowledge reasoning.Finally,this paper applies the logical research re-sults to incomplete formal contexts by introducing two types of implication forms,namely ↓ ↓-type implication and ↑ ↑-type implication,which are both compatible and more stringent than acceptable implication.The compatible canonical bases of the two types of implications are constructed and their completeness and non-redundancy are verified.
万方数据
维普
