Negation as failure. II

AbstractThe use of the negation as failure rule in logic programming is often considered to be tantamount to reasoning from Clark's “completed data base” [2]. Continuing the investigations of Clark and Shepherdson [2,7], we show that this is not fully equivalent to negation as failure either using classical logic or the more appropriate intuitionistic logic. We doubt whether there is any simple and useful logical meaning of negation as failure in the general case, and study in detail some special kinds of data base where the relationship of the completed data base to negation as failure is closer, e.g. where the data base is definite Horn or hierarchic