On Normal Forms and Equivalence for Logic Programs.
James Harland · 1992
It is known that larger classes of formulae than Horn clauses may be used as logic programming languages. One such class of formulae is hereditary Harrop formulae, for which an operational notion of provability has been studied, and it is known that operational provability corresponds to provability in intuitionistic logic. In this paper we discuss the notion of a normal form for this class of formulae, and show how this may be given by removing disjunctions and existential quantifications from programs. Whilst the normal form of the program preserves operational provability, there are operationally equivalent programs which are not intuitionistically equivalent. As it is known that classical logic is too strong to precisely capture operational provability for larger classes of programs than Horn clauses, the appropriate logic in which to study questions of equivalence is an intermediate logic. We explore the nature of the required logic, and show that this may be obtained by the addit...