Some Issues Concerning Fixed Points in Computational Logic Quasi Metrics Multivalued Mappings and the Knaster Tarski Theorem

Many questions concerning the semantics of disjunctive databases and of logic pro gramming systems depend on the xed points of various multivalued mappings and operators determined by the database or program We discuss known versions for mul tivalued mappings of the Knaster Tarski theorem and of the Banach contraction map ping theorem and formulate a version of the classical xed point theorem sometimes attributed to Kleene which is new All these results have applications to the semantics of disjunctive logic programs and we will describe a class of programs to which the new theorem can be applied We also show that a uni cation of the latter two theorems is possible using quasi metrics which parallels the well known uni cation of Rutten and Smyth in the case of conventional programming language semantics MSC Subject Classi cations H N