Category Archives: Formal Languages

Theme One Program • Discussion 1

Posted on March 23, 2018 by Jon Awbrey

Re: Laws Of Form • Armahedi Mahzar AM:  Why do you need XOR in your inquiry system? Clearly we need a way to represent exclusive disjunction, along with its dual, logical equivalence, in any calculus capable of covering propositional logic, … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Theme One • A Program Of Inquiry 10

Posted on March 18, 2018 by Jon Awbrey

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 but overlapping subsets of the broader species of cacti.  Accordingly we … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 9

Posted on March 14, 2018 by Jon Awbrey

We have seen how to take an abstract logical graph of a sort a person might have in mind to represent a logical state of affairs and translate it into a string of characters a computer can translate into a … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 8

Posted on March 10, 2018 by Jon Awbrey

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 →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Theme One • A Program Of Inquiry 7

Posted on March 3, 2018 by Jon Awbrey

Re: Peirce List • (1) • (2) Discussion arose in the Laws Of Form Group about computational explorations of George Spencer Brown’s calculus of indications. Readers of Peirce are generally aware Spencer Brown revived certain aspects of Peirce’s logical graphs, focusing on … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 8 Comments

Theme One • A Program Of Inquiry 6

Posted on February 28, 2018 by Jon Awbrey

Programs are algorithms operating on data structures (Niklaus Wirth).  How do we turn abstract graphs like those used by Charles S. Peirce and G. Spencer Brown into concrete data structures algorithms can manipulate?  There are many ways to do this, but one … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Theme One • A Program Of Inquiry 5

Posted on February 27, 2018 by Jon Awbrey

I started learning programming about the same time I first ran across C.S. Peirce’s Logical Graphs and Spencer Brown’s Laws of Form in the late 1960s and naturally tried each new language and each new set of skills I learned on writing … Continue reading →

Posted in Artificial Intelligence, C.S. Peirce, Cognition, Computation, Constraint Satisfaction Problems, Cybernetics, Formal Languages, Inquiry, Inquiry Driven Systems, Intelligent Systems, Learning Theory, Logic, Peirce, Semiotics | Tagged , , , , , , , , , , , , , | 9 Comments

Survey of Theme One Program • 2

Posted on February 25, 2018 by Jon Awbrey

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 to support an integrated learning and reasoning interface, … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Cognition, Computation, 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, Peirce, Propositional Calculus, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 20 Comments

The Difference That Makes A Difference That Peirce Makes • 18

Posted on July 24, 2017 by Jon Awbrey

Re: Peter Smith • Which Is The Quantifier? From a functional logic point of view logicians slipped a step backward when they passed from Peirce’s and to the current convention of using and for logical quantifiers.  There’s a rough indication … Continue reading →

Posted in C.S. Peirce, Category Theory, Complementarity, Duality, Formal Languages, Higher Order Propositions, Indicator Functions, Inquiry, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Pragmatism, Predicate Calculus, Propositional Calculus, Propositions, Quantifiers, Relation Theory, Semiotics, Type Theory, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 17

Posted on June 26, 2017 by Jon Awbrey

Re: Peirce List • JA • GF • JFS • JLRC • JA • JFS • GF A rather amusing, if slightly ominous illustration of the point I am trying to make here has just popped up in the daily … Continue reading →

Posted in Automata, C.S. Peirce, Category Theory, Chomsky, Complementarity, Dewey, Formal Languages, Inquiry, Laws of Form, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relation Theory, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment