Revisit Boolean Lattice based Fuzzy Description Logic

Fuzzy description logics are a family of logics which allow the representation of (and the reasoning within) structured knowledge affected by uncertainty and vagueness. A well studied solution is to extend description logics with fuzzy sets theory. To solve implication problems in this kind of fuzzy description logics, Boolean lattice based fuzzy description logics is revisited. This paper shows that compared with fuzzy sets based fuzzy description logics, the new formalism not only eliminates the counter-intuitive implication problem, but also possesses simply and efficient reasoning algorithms. Boolean lattice based fuzzy description logic also find its potential application in debugging knowledge base and distributed fuzzy description logics.