A Clausal Form for the Completion of Logic Programs

The Clark completion of a program is a way of making explicit the inferences which may be made from the program using the Negation as Failure (NAF) rule. This may be thought of as adding negative information to the program in such a way that an atom fails ii its negation is derivable from the completion of the program. We show how the completion process may be extended to hereditary Harrop formulae, a class of formulae that properly includes Horn clauses, and, more importantly, that the completion of a hereditary Harrop formulae program may be expressed as a hereditary Harrop formulae program. In this way the richer framework of hereditary Harrop formulae allows the completion to be given in a more explicit form than that of Clark. This also allows the completion to be seen as a set of clauses, i.e. a program, rather than just as a formula of rst-order logic. With the restriction that programs are locally consistent, we show that the completion behaves as expected, in that the computational properties of the program and its completion correspond precisely.