Lukasiewicz logic based Prolog

Prolog is a programming language based on a restricted subset of classical first order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a Lukasiewicz logic based Prolog system. The use of Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting the truth values as relative distance to contradiction. We also present the software tool LULOG which is based on the theoretical results of this paper and can be seen as a Prolog system for many--valued logic. Applications of LULOG to an Ulam game and an example of reasoning with imperfect knowledge are also discussed.