Category Archives: Learning Theory

Re: Systems Science • Joseph Simpson Let me step back and talk about the research intention driving this work. In a very real sense everything I’ve been doing along this line of inquiry for the last fifty years falls within … Continue reading →

What I’m doing this summer … Eighteen years living in the same place and we blissfully forgot what it takes to pack up a house and find a new one.  Thankfully most of the renovation work is done but it’s … Continue reading →

Re: Systems Science • Joseph Simpson Warfield gets it right about the relationship between object languages and metalanguages.  Something about the prefix meta- has contributed to a not uncommon misconception that metalanguages are formalized to a higher degree than the … Continue reading →

Coding Logical Graphs My earliest experiments coding logical graphs as dynamic “pointer” data structures taught me that conceptual and computational efficiencies of a critical sort could be achieved by generalizing their abstract graphs from trees to the variety graph theorists … Continue reading →

The previous post described the elementary data structure used to represent nodes of graphs in the Theme One program.  This post describes the specific family of graphs employed by the program. Figure 1 shows a typical example of a painted … Continue reading →

Theme One is a program for building and transforming a particular species of graph-theoretic data structures, forms designed to support a variety of fundamental learning and reasoning tasks. The program evolved over the course of an exploration into the integration … Continue reading →

It looks like my time will be at the mercy of contractors and realtors most of the summer but I’ll continue with the informal exposition as time permits.  I’ve also returned to work on the formal documentation, organizing the commentary … Continue reading →

An unexpected benefit of cleaning out our basement and putting our belongings in storage was finding a trove of work I thought I’d lost, in a stash of 3½ inch floppies, no less.  I uploaded a sample to a couple of folders … Continue reading →

As an alternative to piling generalities on generalities, not that there’s anything wrong with that, it also helps to look at issues as they arise in concrete applications. One of the most concrete applications I ever attempted was the program … Continue reading →

Logical Cacti (cont.) The abstract character of the cactus language relative to its logical interpretations makes it possible to give abstract rules of equivalence for transforming cacti among themselves and partitioning the space of cacti into formal equivalence classes.  The … Continue reading →