Logical Research On Mixed Decision Implication In Formal Context

Formal Concept Analysis(FCA)is a data analysis tool proposed by Wille for knowledge representation and reasoning in formal context.In FCA,the study of knowledge acquisition is equivalent to the study of(attribute)implication,and decision implication is a form of knowledge representation and reasoning based on implication.Decision implication reduces the redundancy of knowledge extracted from data,and the semantical and syntactical system of decision implication can ensure that sound and complete decision knowledge can be obtained from data,and that sound decision knowledg e can be inferred from existing decision implications.Although decision implication can completely represent and extract decision knowledge from data,there is still information loss.Logic-type decision implication contains stronger knowledge representation ability,but there are problems such as complex decision knowledge construction and quantitative redundancy.Therefore,on the basis of decision implication,this paper proposes mixed decision implication,which not only enhances the knowledge representation ability of decision implication,but also solves the problems existing in logic-type decision implication,and has a more concise and complete knowledge representation and reasoning ability.The main research contents and innovative results are as follows.(1)Mixed decision implication is proposed,and complete semantical and semantical structure systems of mixed decision implication are constructed.Negative attributes are introduced into decision implication,so that decision implication has the ability to extract negative knowledge from data.From the perspective of data,the problems of attribute contradiction after introducing negative attributes are studied,and the method of extracting decision knowledge from mixed decision context is given.In terms of semantics,the concepts of logical self-consistency and semantical deduction are given to ensure that sound mixed decision implication can be obtained based on the existing decision knowledge,avoiding the possible contradiction in knowledge reasoning and laying the foundation for further obtaining complete and non-redundant.In terms of semantics,soundness and completeness of knowledge representation and reasoning are ensured,and possible contradictions in knowledge reasoning are avoided.In terms of syntactics,Mixed Augmentation and Mixed Combination are proposed,and soundness,completeness and non-redundancy of the two mixed inference rules are proved to improve the efficiency of knowledge reasoning.(2)The knowledge representation capability of mixed decision implication and logictype decision implication is studied.First,the relationships between the attribute set in mixed decision implication and the logical formulas of logic-type decision implication are analyzed.Second,four representations of logic-type decision implication in data are studied,and it is clarified that mixed decision implication is a special form of logic-type decision implication under the logic-type decision implication system.Finally,it is proven that mixed decision implication is complete with respect to logic-type decision implication,i.e.,the semantical equivalence of mixed decision implication and logic-type decision implication,and it is further shown that logic-type decision implication can be equivalently implemented by mixed decision implication,which effectively solves the complexity of decision knowledge construction and the quantitative redundancy of decision knowledge in logictype decision implication.