Unifying Cycles

trum f ¨ ur K ¨ unstliche Intelligenz, DFKI) with sites in Kaiserslautern and Saarbrücken is a non-profit organization which was founded in 1988. The shareholder com-search projects conducted at the DFKI are funded by the German Ministry for Research and Technology, by the shareholder companies, or by other industrial contracts. The DFKI conducts application-oriented basic research in the field of artificial intelligence and other related subfields of computer science. The overall goal is to construct systems with technical knowledge and common sense which-by using AI methods-implement a problem solution for a selected application area. Currently, there are the following research areas at the DFKI: The DFKI strives at making its research results available to the scientific community. There exist many contacts to domestic and foreign research institutions, both in academy and industry. The DFKI hosts technology transfer workshops for shareholders and other interested groups in order to inform about the current state of research. From its beginning, the DFKI has provided an attractive working environment for AI researchers from Germany and from all over the world. The goal is to have a staff of about 100 researchers at the end of the building-up phase. c Deutsches Forschungszentrum für K ¨ unstliche Intelligenz 1992 This work may not be copied or reproduced in whole of part for any commercial purpose. Permission to copy in whole or part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of the Deutsche Forschungszentrum für K ¨ unstliche Intelligenz, Kaiserslautern, Federal Republic of Germany; an acknowledgement of the authors and individual contributors to the work; all applicable portions of this copyright notice. Copying, reproducing, or republishing for any other purpose shall require a licence with payment of fee to Deutsches Forschungszentrum für K ¨ unstliche Intelligenz. Abstract Two-literal clauses of the form L R occur quite frequently in logic programs, deductive databases, and|disguised as an equation|in term rewriting systems. These clauses deene a cycle if the atoms L and R are weakly uniiable, i.e., if L uniies with a new variant of R. The obvious problem with cycles is to control the number of iterations through the cycle. In this paper we consider the cycle uniication problem of unifying two literals G and F modulo a cycle. We review the state of …