Some Issues Concerning Fixed-Points in Computational Logic.
by
Anthony Seda
Mathematics, University College Cork, Cork, Ireland.
Coauthors: Pascal Hitzler (University College Cork)

Many questions concerned with the semantics of disjunctive databases and of logic programming systems depend on the fixed points of various multivalued mappings and operators determined by the database or program. In this talk, we discuss recent work of the authors in relation to fixed points in the following contexts: (1) A fixed-point theorem using quasi-metrics, analogous to the Rutten-Smyth theorem, which includes known versions of both the Knaster-Tarski and Banach contraction mapping theorem for multivalued mappings (both of which have been applied to disjunctive databases). (2) The determination of classes of programs with the following properties: (i) that each program in the class has a unique fixed point of its corresponding operator (i.e. a unique supported model), and (ii) the class is computationally adequate in that it can compute all partial recursive functions. Various methods have been considered by the authors for obtaining such classes including ideas from domain theory and, more recently, the use of three-valued logics. If time permits, we will also consider this work in relationship to termination proofs from the point of view of topology.

Date received: June 15, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-79.