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Transformations of Logical Graphs • 10
Semiotic Transformations Re: Transformations of Logical Graphs • (4) • (5) • (6) • (7) • (8) • (9) After the four orbits of self‑dual logical graphs we come to six orbits of dual pairs. In no...
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Transformations of Logical Graphs • 11
Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) Continuing our scan of the Table in Episode 8, the next two orbits contain the logical graphs for the boolean functions...
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Transformations of Logical Graphs • 12
Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) Re: Interpretive Duality as Sign Relation • Orbit Order Taking from our wallets an old schedule of orbits from...
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Transformations of Logical Graphs • 13
Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) • (12) Continuing our scan of the Table in Episode 8, the next orbit contains the logical graphs for the boolean...
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Transformations of Logical Graphs • 14
Semiotic Transformations Re: Transformations of Logical Graphs • (8) • (9) • (10) • (11) • (12) • (13) Completing our scan of the Table in Episode 8, the last orbit up for consideration contains the...
View ArticleTransformations of Logical Graphs • Discussion 1
Re: Laws of Form • Mauro Bertani Dear Mauro, The couple of pages linked below give the clearest and quickest introduction I’ve been able to manage so far when it comes to the elements of logical...
View ArticleTheme One Program • Motivation 1
The main idea behind the Theme One program is the efficient use of graph-theoretic data structures for the tasks of “learning” and “reasoning”. I am thinking of learning in the sense of learning about...
View ArticleTheme One Program • Motivation 2
A side‑effect of working on the Theme One program over the course of a decade was the measure of insight it gave me into the reasons why empiricists and rationalists have so much trouble understanding...
View ArticleTheme One Program • Motivation 3
Sometime around 1970 John B. Eulenberg came from Stanford to direct Michigan State’s Artificial Language Lab, where I would come to spend many interesting hours hanging out all through the 70s and 80s....
View ArticleTheme One Program • Motivation 4
From Zipf’s Law and the category of “things that vary inversely with frequency” I got my first brush with the idea that keeping track of usage frequencies is part and parcel of building efficient...
View ArticleTheme One Program • Motivation 5
Since I’m working from decades‑old memories of first inklings I thought I might peruse the web for current information about Zipf’s Law. I see there is now something called the Zipf–Mandelbrot (and...
View ArticleTheme One Program • Motivation 6
Comments I made in reply to a correspondent’s questions about delimiters and tokenizing in the Learner module may be worth sharing here. In one of the projects I submitted toward a Master’s in...
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Theme One Program • Exposition 1
Theme One is a program for constructing and transforming a particular species of graph‑theoretic data structures, forms designed to support a variety of fundamental learning and reasoning tasks. The...
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Theme One Program • Exposition 2
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. Painted...
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Theme One Program • Exposition 3
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...
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Theme One Program • Exposition 4
Parsing Logical Graphs It is possible to write a program that parses cactus expressions into reasonable facsimiles of cactus graphs as pointer structures in computer memory, making edges correspond to...
View ArticleTheme One Program • Exposition 5
Lexical, Literal, Logical Theme One puts cactus graphs to work in three distinct but related ways, called lexical, literal, and logical applications. The three modes of operation employ three distinct...
View ArticleTheme One Program • Exposition 6
Quickly recapping the discussion so far, we started with a data structure called an idea‑form flag and adopted it as a building block for constructing a species of graph-theoretic data structures...
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Theme One Program • Exposition 7
Logical Cacti Up till now we’ve been working to hammer out a two‑edged sword of syntax, honing the syntax of cactus graphs and cactus expressions and turning it to use in taming the syntax of two‑level...
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Theme One Program • Exposition 8
Mathematical Structure and Logical Interpretation The main things to take away from the previous post are the following two ideas, one syntactic and one semantic. The compositional structures of cactus...
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