A linear semantics for allowed logic programs

A declarative semantics for the class of allowed logic programs is proposed. Such a semantics is a logical theory, the linear completion of the program P, which differs from Clark´s completion because the underlying logic is linear logic rather than classical logic. With respect to such a semantics, the soundness and completeness of SLDNF-resolution is proven. That is, it is proven that the computational notion of success of an allowed query Q for an allowed program P corresponds to the provability of an instantiation of Q in the linear completion of P, and the notion of failure to the provability of the (linear) negation of Q in the linear completion of P