We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of left terminating positive programs by means of the notion of an acceptable program that provides us with a practical method of proving termination. The method is illustrated by giving a simple proof of termination of the quicksort program for the desired class of goals. Then we extend this approach to the class of general logic programs by modifying the concept of acceptability. We prove that acceptable general programs are left terminating. The converse implication does not hold but we show that under the assumption of nonfloundering from ground goals every left terminating general program is acceptable. Finally, we prove that various ways of defining semantics coincide for acceptable gen...

We provide simple conditions which allow us to conclude that in case of several well-known Prolog programs the unification algorithm can be replaced by iterated matching. The main tools used here are types and generic expressions for types. As already noticed by other researchers, such a replacement offers a possibility of improving the efficiency of program's execution.

We try to assess to what extent declarative programming can be realized in Prolog and which aspects of correctness of Prolog programs can be dealt with by means of declarative interpretation. More specifically, we shall discuss termination of Prolog programs, partial correctness, absence of errors and the safe use of negation. 1991 Mathematics Subject Classification: 68Q40, 68T15. CR Categories: F.3.2., F.4.1, H.3.3, I.2.3. Keywords and Phrases: declarative programming, Prolog programs, verification. Notes. This research was partly supported by the ESPRIT Basic Research Action 6810 (Compulog 2). This paper will appear as invited lecture in: Proc. of International Logic Programming Symposium (ILPS '93), The MIT Press, D. Miller (editor). It also appeared as a Technical Report No CT-93-06 in the ILLC Prepublication Series of the University of Amsterdam. 1