The Essential Inadequacy of Deduction in Logic Programming

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 includes at least one function symbol, an individual constant. We let PK denote the set of all (normal) logic programs over K, let F denote the set of all function symbols in K, and let UF denote the set of all ground terms over F . All concepts from the foundations of logic programming not explicitly defined in this paper may be found in Lloyd [1]. 2 Inadequacy of deduction procedure