Logic programs, iterated function systems, and recurrent radial basis function networks
Logic programs, iterated function systems, and recurrent radial basis function networks
复制标题
DOI：
10.1016/j.jal.2004.03.003
复制
发表时间：
2004-09
期刊：
影响因子：
--
通讯作者：
Sebastian Bader;P. Hitzler
中科院分区：
文献类型：
--
作者：
Sebastian Bader;P. Hitzler
在真实的平面中显示的一阶逻辑程序的单步算子的图展示了从拓扑动力学已知的自相似结构，即，它们似乎是分形，或者更准确地说，是迭代函数系统的吸引子。我们表明，这种观察可以在数学上精确。特别是，我们给出的条件，确保这些图符合适当选择的迭代函数系统的吸引子，和条件，允许这样的图的迭代函数系统或分形插值的近似。由于迭代函数系统可以很容易地使用递归径向基函数网络进行编码，我们最终获得了在函数符号存在的情况下近似逻辑程序的连接主义系统。
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.