N-Prolog: An Extension of Prolog with Hypothetical Implication II - Logical Foundations, and Negation as Failure

We shall see that success in the N-PROLOG computation of a goal G from the database P means logically that P h G in intuitionistic logic. We will also introduce an additional computational rule called the restart rule (allowing one to replace, at any time of the computation, the current goal by the original goal). Success of an onginal goal G from a database P through a computation in N-PROLOG with the restart rule means that P IG in classical logic. The restart rule can be modified to yield many logics intermediate between classical and intuitionistic logic. In my lecture notes [1], I use these ideas to present classical logic procedurally, in a PROLOG-hke way. My paper with K. Broda and F. Kriwaczek [2] describes a theorem prover based on these ideas and compares this theorem prover with SL resolution and other forms of resolution. Modal and temporal logics can also be represented in N-PROLOG in certain ways, and especially appUed to database deletion, temporal updating, and management. This will be dealt with in paper III of this series.