Topological Investigations of the Operators of the Well-Founded, and Alternating Fixed-Point Semantics of Normal Logic Programs

Abstract

We present a progress report on ongoing work to investigate topologies on spaces of interpretations in which one obtains the continuity of the operators associated with the well-founded, and alternating fixed-point semantics of a normal logic program. This work parallels that of Batarekh, Subrahmanian, Hitzler and Seda on the corresponding question in relation to supported models. In particular, its ultimate objective is to parallel the work of Hitzler and Seda in simplifying the construction of the perfect model of a locally stratified program by giving better understanding of the well-founded model. Our results are preliminary in that we consider only the Scott and Cantor topologies and close relatives of these, and are partial in that they suggest that a more subtle analysis of convergence is needed which closely reflects the properties of the well-founded model.