  We present a novel unity of logic, viz., a single sequent calculus that
embodies classical, intuitionistic and linear logics. Concretely, we define
classical linear logic negative (CLL$^-$), a new logic that is classical and
linear yet discards the polarities and the strict De Morgan laws in classical
linear logic (CLL). Then, we define unlinearisation and classicalisation on
sequent calculi such that unlinearisation maps CLL$^-$ (resp. intuitionistic
linear logic (ILL)) to classical logic (CL) (resp. intuitionistic logic (IL)),
and classicalisation maps IL (resp. ILL) to CL (resp. CLL$^-$) modulo
conservative extensions. By these two maps, only a sequent calculus for a
conservative extension of ILL suffices for ILL, IL, CLL$^-$ and CL. This result
achieves a simple, highly systematic unity of logic by discarding the
polarities and the strict De Morgan laws, which (arguably) only CLL has, and
consisting of the uniform classicalisation and unlinearisation, which commute.
Previous methods do not satisfy these points. Our unity also clarifies the
dichotomies between intuitionisity and classicality, and between linearity and
non-linearity of logic, which are symmetric.
