The notion of partial deduction known from logic programming is deened in the framework of Structural Synthesis of Programs (SSP). Partial deduction for computability statements in SSP is deened. Completeness and correctness of partial deduction in the framework of SSP are proven. Several tactics and stopping criteria are suggested.

Natural deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused natural deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear natural deduction and the backward linear focusing calculus.

1 Introduction In this paper we provide very broad notions of deduction and consequence for logic programs (so-called LP-deduction relations and LP-consequence relations), and we prove that under very modest assumptions, an LP-deduction relation will be either unsound or incomplete with respect to every LP-consequence relation. Throughout this paper we assume a non-logical alphabet, K, which in...