Category Archives: Equational Inference

Survey of Theme One Program • 1

This is a Survey of previous blog and wiki posts on the Theme One Program that I worked on all through the 1980s. The aim of the project was to develop fundamental algorithms and data structures to support an integrated … Continue reading

Posted in Algorithms, Animata, Artificial Intelligence, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Cognitive Science, Computation, Computational Complexity, Computer Science, Computing, Constraint Satisfaction Problems, Cybernetics, Data Structures, Diagrammatic Reasoning, Diagrams, Differential Analytic Turing Automata, Education, Educational Systems Design, Educational Technology, Equational Inference, Functional Logic, Graph Theory, Indicator Functions, Inquiry, Inquiry Driven Education, Inquiry Driven Systems, Inquiry Into Inquiry, Intelligent Systems, Knowledge, Learning, Learning Theory, Logic, Logical Graphs, Machine Learning, Mathematics, Mental Models, Minimal Negation Operators, Painted Cacti, Peirce, Programming, Programming Languages, Propositional Calculus, Propositional Equation Reasoning Systems, Propositions, Research Technology, Semeiosis, Semiosis, Semiotics, Sign Relations, Surveys, Teaching, Theorem Proving, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Precursors Of Category Theory • 1

A few years ago I began a sketch on the Precursors of Category Theory, aiming to trace the continuities of the category concept from Aristotle, to Kant and Peirce, through Hilbert and Ackermann, to contemporary mathematical practice. This post is … Continue reading

Posted in Abstraction, Ackermann, Analogy, Aristotle, Carnap, Category Theory, Diagrammatic Reasoning, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Iconicity, Kant, Logic, Mathematics, Mental Models, Peirce, Propositions As Types Analogy, Saunders Mac Lane, Surveys, Triadic Relations, Type Theory, Universals, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Survey of Differential Logic • 1

This is a Survey of previous blog and wiki posts on Differential Logic, material that I plan to develop toward a more compact and systematic account. Elements Differential Logic • Introduction Differential Propositional Calculus Architectonics Minimal Negation Operator Cactus Language … Continue reading

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamical Systems, Equational Inference, Frankl Conjecture, Functional Logic, Graph Theory, Hill Climbing, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Surveys, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Animated Logical Graphs • 1

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading

Posted in Abstraction, Amphecks, Animata, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Surveys, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Alpha Now, Omega Later : 4

Re: Cristopher Moore on Theorems From Physics? It is critically important to distinguish between the objective landscape, the boolean functions as mathematical objects, and the syntactic landscape, the particular formal language we are using as a propositional calculus to denote … Continue reading

Posted in Computational Complexity, Differential Logic, Equational Inference, Fixation of Belief, General Problem Solver, Hill Climbing, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Peirce, Peirce List, Physics, Propositional Calculus, Scientific Inquiry, Scientific Method, Semiotics, Sisyphus, Spencer Brown, Systems Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Alpha Now, Omega Later : 3

Re: Theorems From Physics? Bits of Synchronicity … What kind of information process is scientific inquiry? What kinds of information process are involved in the various types of inference — abductive, deductive, inductive — that go to make up scientific … Continue reading

Posted in Differential Logic, Equational Inference, Fixation of Belief, Inquiry, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Peirce, Peirce List, Physics, Propositional Calculus, Scientific Inquiry, Scientific Method, Semiotics, Spencer Brown, Systems Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , | 1 Comment

Alpha Now, Omega Later : 2

It’s been a while since I threaded this thread — and then there were all the delightful distractions of the holiday convergence — so let me refresh my memory as to what drew me back to these environs. I’m still … Continue reading

Posted in Differential Logic, Equational Inference, Inquiry Driven Systems, Laws of Form, Logic, Logical Graphs, Peirce, Peirce List, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Systems Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , | 1 Comment