Document Type

Article

Publication Date

9-1-2004

Abstract

Graphs of the single-step operator for first-order logic programs—displayed in the real plane—exhibit self-similar structures known from topological dynamics, i.e., they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which approximate logic programs in the presence of function symbols.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in the Journal of Applied Logic. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the Journal of Applied Logic, VOL 2, ISSUE 3 (Sep. 2004), DOI: 10.1016/j.jal.2004.03.003.

DOI

10.1016/j.jal.2004.03.003