01805nas a2200121 4500008004100000245007300041210006900114260006400183520136100247100002201608700002001630856003301650 1999 eng d00aMultivalued Mappings, Fixed-Point Theorems and Disjunctive Databases0 aMultivalued Mappings FixedPoint Theorems and Disjunctive Databas bElectronic Workshops in Computing, British Computer Society3 aIn this paper, we discuss the semantics of disjunctive programs and databases and show how multivalued mappings and their fixed points arise naturally within this context. A number of fixed-point theorems for multivalued mappings are considered, some of which are already known and some of which are new. The notion of a normal derivative of a disjunctive program is introduced. Normal derivatives are normal logic programs which are determined by the disjunctive program. Thus, the well-known single-step operator associated with a normal derivative is single-valued, and its fixed points can be found by well-established means. It is shown how fixed points of the multivalued mapping determined by a disjunctive program relate to the fixed points of the single-step operators coming from its normal derivatives. This procedure has potential for simplifying the construction of models of disjunctive databases, and this point is discussed. Most of the results for multivalued mappings rest on corresponding, known results concerning fixed points of single-valued mappings. Since the latter results are frequently referred to, they have been collected together for convenience in a survey which should be of independent interest as well as being preparatory for the later results. Finally, a number of problems and issues raised by this work are discussed.1 aSeda, Anthony, K.1 aHitzler, Pascal uhttp://knoesis.org/node/1802