Adding Negation to Lambda Mu

We present $\cal L$, an extension of Parigot's $\lambda\mu$-calculus by adding negation as a type constructor, together with syntactic constructs that represent introduction and elimination. will define notion reduction extends $\lambda\mu$'s system two new rules, show the satisfies subject reduction. Using Aczel's generalisation Tait Martin-L\"of's parallel reduction, we this extended is confluent. Although assignment has its limitations respect to representation proofs in natural deduction implication negation, all propositions can be shown there have witness L$. Girard's approach reducibility candidates, typeable terms are strongly normalisable, conclude paper showing for L$ enjoys principal typing property.