Tag Archives: Logical Graphs

Unknown's avatar Jon Awbrey 7:16 am on November 20, 2025
Tags: Algorithms, , , , , , , , Data Structures, , , , , , , , , Logical Graphs, , , , , , ,   

Survey of Theme One Program • 7

This is a Survey of resources 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 had earlier developed separate programs for basic components of those tasks, in particular, two‑level formal language learning and propositional constraint satisfaction, the latter using an extension of C.S. Peirce’s logical graphs as a syntax for propositional logic.  Thus arose the question of how well it might be possible to get “empiricist” and “rationalist” modes of operation to cooperate.  The long‑term vision is the implementation of an Automated Research Tool able to double as a platform for Inquiry Driven Education.

Wiki Hub

Documentation

Blog Series

Blog Dialogs

Applications

References

  • Awbrey, S.M., and Awbrey, J.L. (May 1991), “An Architecture for Inquiry • Building Computer Platforms for Discovery”, Proceedings of the Eighth International Conference on Technology and Education, Toronto, Canada, pp. 874–875.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (January 1991), “Exploring Research Data Interactively • Developing a Computer Architecture for Inquiry”, Poster presented at the Annual Sigma Xi Research Forum, University of Texas Medical Branch, Galveston, TX.
  • Awbrey, J.L., and Awbrey, S.M. (August 1990), “Exploring Research Data Interactively • Theme One : A Program of Inquiry”, Proceedings of the Sixth Annual Conference on Applications of Artificial Intelligence and CD-ROM in Education and Training, Society for Applied Learning Technology, Washington, DC, pp. 9–15.  Online.

cc: FB | Theme One Program • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#algorithms, #animata, #artificial-intelligence, #automated-research-tools, #boolean-functions, #c-s-peirce, #cactus-graphs, #constraint-satisfaction-problems, #data-structures, #differential-logic, #equational-inference, #formal-languages, #graph-theory, #inquiry-driven-systems, #laws-of-form, #learning-theory, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #painted-cacti, #propositional-calculus, #propositional-equation-reasoning-systems, #spencer-brown, #visualization

Unknown's avatar Jon Awbrey 11:30 am on November 15, 2025
Tags: , , , , , , Computational Complexity, , , , , , , , Logical Graphs, , , , , , Proof Theory, , , , Theorem Proving,   

Survey of Animated Logical Graphs • 8

This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.

Beginnings

Elements

Examples

Blog Series

  • Logical Graphs • Interpretive Duality • (1) • (2) • (3) • (4)
  • Logical Graphs, Iconicity, Interpretation • (1) • (2)
  • Genus, Species, Pie Charts, Radio Buttons • (1)

Excursions

Applications

Anamnesis

cc: FB | Logical Graphs • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#amphecks, #animata, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #computational-complexity, #constraint-satisfaction-problems, #differential-logic, #equational-inference, #graph-theory, #group-theory, #laws-of-form, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #model-theory, #painted-cacti, #peirce, #proof-theory, #propositional-calculus, #propositional-equation-reasoning-systems, #spencer-brown, #theorem-proving, #visualization

Unknown's avatar Jon Awbrey 11:48 am on November 9, 2025
Tags: Algebra, Algebra of Logic, , , Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, , , , , , , Logical Graphs, , , , , Set Theory, , , ,   

Survey of Relation Theory • 9

In the present Survey of blog and wiki resources for Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set‑theoretic constructions, many of which arise quite naturally in applications.  This approach to relation theory is distinct from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other.

Elements

Relational Concepts

Relation Composition Relation Construction Relation Reduction
Relative Term Sign Relation Triadic Relation
Logic of Relatives Hypostatic Abstraction Continuous Predicate

Illustrations

Information‑Theoretic Perspective

  • Mathematical Demonstration and the Doctrine of Individuals • (1) • (2)

Blog Series

Peirce’s 1870 “Logic of Relatives”

Peirce’s 1880 “Algebra of Logic” Chapter 3

Peirce’s 1885 “Algebra of Logic”

  • C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • (1) • (2)
  • C.S. Peirce • Algebra of Logic 1885 • Selections • (1) • (2) • (3) • (4)

Resources

cc: FB | Relation Theory • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#algebra, #algebra-of-logic, #c-s-peirce, #category-theory, #combinatorics, #discrete-mathematics, #duality, #dyadic-relations, #formal-languages, #foundations-of-mathematics, #graph-theory, #group-theory, #logic, #logic-of-relatives, #logical-graphs, #mathematics, #model-theory, #relation-theory, #semiotics, #set-theory, #sign-relational-manifolds, #sign-relations, #triadic-relations, #type-theory

Unknown's avatar Jon Awbrey 11:20 am on November 7, 2025
Tags: , , , , , , , Change, , Differential Analytic Turing Automata, Differential Calculus, , Discrete Dynamics, , Frankl Conjecture, , Gradient Descent, , Hologrammautomaton, , Leibniz, , Logical Graphs, , , ,   

Survey of Differential Logic • 8

This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.

Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description.  A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models.  To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.

Elements

Blog Series

Architectonics

Applications

Blog Dialogs

Explorations

cc: FB | Differential Logic • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

#amphecks, #animata, #boolean-algebra, #boolean-functions, #c-s-peirce, #cactus-graphs, #category-theory, #change, #cybernetics, #differential-analytic-turing-automata, #differential-calculus, #differential-logic, #discrete-dynamics, #equational-inference, #frankl-conjecture, #functional-logic, #gradient-descent, #graph-theory, #hologrammautomaton, #inquiry-driven-systems, #leibniz, #logic, #logical-graphs, #mathematics, #minimal-negation-operators, #propositional-calculus, #visualization