Monthly Archives: August 2020

Survey of Theme One Program • 3

Posted on August 28, 2020 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 for integrating empirical learning with logical reasoning. I … 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 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 | 40 Comments

Animated Logical Graphs • 38

Posted on August 25, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs Three examples of propositional proofs in logical graphs using equational inference rules can be found at the following location. Propositional Equation Reasoning Systems • Exemplary Proofs Animated proofs of the three … 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 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 | 8 Comments

Survey of Animated Logical Graphs • 3

Posted on August 23, 2020 by Jon Awbrey

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 Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Differential Logic, 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 Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Constraint Satisfaction Problems, Differential Logic, 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 | 26 Comments

Animated Logical Graphs • 37

Posted on August 22, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs Another dimension of proof style has to do with how much information is kept or lost as the argument develops. For the moment let’s focus on classical deductive reasoning at the … Continue reading →

Animated Logical Graphs • 36

Posted on August 21, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs Dear Dick, You asked, “Is this measure, the logical flow of a proof, of any interest?” I was not sure how you define the measure of flow in a proof — … Continue reading →

Animated Logical Graphs • 35

Posted on August 19, 2020 by Jon Awbrey

Re: Richard J. Lipton • Logical Complexity Of Proofs The smoothest way I know to do propositional calculus is by using minimal negation operators as primitives, parsing propositional formulas into (painted and rooted) cactus graphs, and using the appropriate extension … Continue reading →

Mathematical Method • Discussion 7

Posted on August 15, 2020 by Jon Awbrey

Re: Ontolog Forum • Alex Shkotin Dear Alex, You raised the following point: AS: One important usage of a sign is as an element of a language, especially a formal one, i.e. with a formal grammar. For context you cited … Continue reading →

Posted in Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Tagged Abstraction, C.S. Peirce, Essentialism, Hypostatic Abstraction, Logic, Mathematics, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Pragmatic Maxim, Pragmatism, Realism, Semiotics, Theory | Leave a comment

Mathematical Method • Discussion 6

Posted on August 13, 2020 by Jon Awbrey

Re: Ontolog Forum • Alex Shkotin Dear Alex, Thanks for the very apt segue from Jon Barwise — Modern mathematics might be described as the science of abstract objects, be they real numbers, functions, surfaces, algebraic structures or whatever. Mathematical … Continue reading →

Animated Logical Graphs • 34

Posted on August 11, 2020 by Jon Awbrey

Re: Ontolog Forum • John Sowa Re: Peirce List • John Sowa Dear John, I can’t imagine why anyone would bother with Peirce’s logic if it’s just Frege and Russell in a different syntax, which has been the opinion I … Continue reading →

Mathematical Method • Discussion 5

Posted on August 10, 2020 by Jon Awbrey

Re: Ontolog Forum • Paul Tyson Dear Paul, “How We Think” is a topic for the descriptive science of psychology, and its ways are legion beyond definitive or exhaustive description. “How We Ought To Think” if we wish to succeed … Continue reading →

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