Tag Archives: Equational Inference

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

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

Animated Logical Graphs • 12

Posted on January 31, 2018 by Jon Awbrey

Re: Facebook Discussion • Meredith Bricken Mills I’ve always been fond of picture proofs — it was one of the things that drew me to graph theory, topology, and the logical graphs of C.S. Peirce and Spencer Brown in the first place.  … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Animated Logical Graphs • 11

Posted on January 30, 2018 by Jon Awbrey

Re: Richard Coyne • Inside Out Logic Venn diagrams make for very iconic representations of their universes of discourse.  That is one of the main sources of their intuitive utility and also the main source of their logical limitations — … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 9 Comments

Animated Logical Graphs • 10

Posted on March 3, 2017 by Jon Awbrey

Re: Peirce List Discussion • Charles Pyle Let’s consider Peirce’s logical graphs at the alpha level, the abstract forms of which can be interpreted for propositional logic.  I say “can be interpreted” advisedly because the system of logical graphs itself … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Animated Logical Graphs • 9

Posted on May 24, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations The insight it takes to find a succinct axiom set for a theoretical domain falls under the heading of abductive or retroductive reasoning, a knack as yet refractory to computational attack, but … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

Animated Logical Graphs • 8

Posted on May 23, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations The most striking example of a “Primitive Insight Proof” (PIP❢) known to me is the Dawes–Utting proof of the Double Negation Theorem from the CSP–GSB axioms for propositional logic.  There is a … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Animated Logical Graphs • 7

Posted on May 22, 2015 by Jon Awbrey

Re: Ken Regan • The Shapes of Computations There are several issues of computation shape and proof style that raise their heads already at the logical ground level of boolean functions and propositional calculus.  From what I’ve seen, there are … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph 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 | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Survey of Theme One Program • 1

Posted on May 18, 2015 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 , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Survey of Precursors Of Category Theory • 1

Posted on May 15, 2015 by Jon Awbrey

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.  A Survey of … Continue reading →

Posted in Abstraction, Ackermann, Analogy, Aristotle, C.S. Peirce, Carnap, Category Theory, Diagrams, Dyadic Relations, Equational Inference, Form, Foundations of Mathematics, Functional Logic, Hilbert, History of Mathematics, Hypostatic Abstraction, Kant, Logic, Logic of Relatives, Mathematics, Peirce, Propositions As Types Analogy, Relation Theory, Saunders Mac Lane, Semiotics, Sign Relations, Surveys, Triadic Relations, Type Theory, Universals | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 18 Comments