# Tag Archives: Logic

## 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. Figure 1 shows a typical example of a painted … Continue reading

## Theme One Program • Exposition 1

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

## Survey of Theme One Program • 4

This is a Survey of blog and wiki posts relating to the Theme One Program I worked on all through the 1980s.  The aim was to develop fundamental algorithms and data structures for integrating empirical learning with logical reasoning.  I … Continue reading

## Functional Logic • Inquiry and Analogy • 21

Inquiry and Analogy • Generalized Umpire Operators To get a better handle on the space of higher order propositions and continue developing our functional approach to quantification theory, we’ll need a number of specialized tools.  To begin, we define a … Continue reading

## Functional Logic • Inquiry and Analogy • 20

Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Table 21 provides a thumbnail sketch of the relationships discussed in this section. Resources Logic Syllabus Boolean Function Boolean-Valued Function Logical Conjunction Minimal Negation Operator Introduction to Inquiry … Continue reading

## Functional Logic • Inquiry and Analogy • 19

Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Reflection is turning a topic over in various aspects and in various lights so that nothing significant about it shall be overlooked — almost as one might turn … Continue reading

## Functional Logic • Inquiry and Analogy • 18

Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Last time we took up a fourfold schema of quantified propositional forms traditionally known as a “Square of Opposition”, relating it to a quartet of higher order propositions … Continue reading

## Functional Logic • Inquiry and Analogy • 17

Inquiry and Analogy • Application of Higher Order Propositions to Quantification Theory Our excursion into the expanding landscape of higher order propositions has come round to the point where we can begin to open up new perspectives on quantificational logic. … Continue reading

## Functional Logic • Inquiry and Analogy • 16

Inquiry and Analogy • Extending the Existential Interpretation to Quantificational Logic One of the resources we have for this work is a formal calculus based on C.S. Peirce’s logical graphs.  For now we’ll adopt the existential interpretation of that calculus, fixing … Continue reading

## Functional Logic • Inquiry and Analogy • 15

Inquiry and Analogy • Measure for Measure Let us define two families of measures, by means of the following equations: Table 14 shows the value of each on each of the 16 boolean functions   In terms of the implication … Continue reading