A Max-Term Counting Based Knowledge Inconsistency Checking Strategy and Inconsistency Measure Calculation of Fuzzy Knowledge Based Systems

Algorithm 1

Finding all the minimal inconsistent subsets of a knowledge base.

Input: a knowledge base

Output: all the minimal inconsistent subsets of knowledge base

Begin

(1) normalize the knowledge base to ensure that every formula contained in it is a clause,

   and denoted it as ;

   initialize to be an empty set of sets;

(2) build a variable Boolean lattice with each node denoting a set of formulas

   (if a node denotes a formula set, then we call it a -degree node), and give each node a unmarked flag;

(3) set up an empty list List, and put all of the 2-degree nodes into List;

   fetch the head Head from List;

   if Head is inconsistent, then  //by using Theorem 7

    Begin

     put Head into ;

     mark all the ancestors of Head;

    End

   else Head is consistent, then

    Begin

     insert all of the un-marked upper neighbors of Head at the front of List;

     mark all the descendants of Head, and if they exist in List, then remove them from List;

    End

(4) return .

End.