Implication algebra by meta-theory of the uncertainty

Lukasiewicz and others created, in a pure conceptual domain, the many valued logic that we can describe, in a symbolic way, by lattice structures. Zadeh, with the definition of the continuous membership function, created Fuzzy Sets for vagueness, the operations of which are different from the usual set theory as intersection, union and complement. L-fuzzy sets are built when the membership function assumes symbolic values L. Meta theory of uncertainty based upon modal logic is built to unify measures of vagueness, uncertainty and inconsistence in natural language. This paper shows the connection between the Meta theory of uncertainty based upon modal logic and the implication algebra.