Category Archives: Propositional Equation Reasoning Systems

Theme One Program • Motivation 4

Posted on May 20, 2018 by Jon Awbrey

From Zipf’s Law and the category of “things that vary inversely to frequency” I got my first brush with the idea that keeping track of usage frequencies is part and parcel of building efficient codes. In its first application the … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Theme One Program • Motivation 3

Posted on May 19, 2018 by Jon Awbrey

Sometime around 1970 John B. Eulenberg came from Stanford to direct Michigan State’s Artificial Language Lab, where I would come to spend many interesting hours hanging out all through the 70s and 80s.  Along with its research program the lab … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Theme One Program • Motivation 2

Posted on May 17, 2018 by Jon Awbrey

A side-effect of working on the Theme One program over the course of a decade was the measure of insight it gave me into the reasons why empiricists and rationalists have so much trouble understanding each other, even when those … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Theme One Program • Motivation 1

Posted on May 15, 2018 by Jon Awbrey

The main idea behind the Theme One program is the efficient use of graph-theoretic data structures for the tasks of “learning” and “reasoning”. I am thinking of learning in the sense of learning about an environment, in essence, gaining information about … Continue reading →

Posted in Algorithms, Animata, Artificial Intelligence, Boolean Functions, C.S. Peirce, Cactus Graphs, Computation, Computational Complexity, Cybernetics, Data Structures, Differential Logic, Form, Formal Languages, Graph Theory, Inquiry, Inquiry Driven Systems, Intelligent Systems, Laws of Form, Learning, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pragmatics, Programming, Propositional Calculus, Propositional Equation Reasoning Systems, Reasoning, Semantics, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 3 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

Differential Logic • Comment 3

Posted on December 30, 2017 by Jon Awbrey

In my previous comment on boundaries in object universes and venn diagrams, and always when I’m being careful about their mathematical senses, the definitions of “topology” and “boundary” I have in mind can be found in any standard textbook.  Here are … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Diagrammatic Reasoning, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Differential Logic • Comment 2

Posted on December 28, 2017 by Jon Awbrey

As always, we have to distinguish between the diagram itself, the representation or sign inscribed in some medium, and the formal object it represents under a given interpretation. A venn diagram is an iconic sign we use to represent a … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Diagrammatic Reasoning, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , | 12 Comments

Differential Logic • Comment 1

Posted on December 21, 2017 by Jon Awbrey

Re: Gil Kalai • Pivotal Variables Just a tangential association with respect to logical influence and pivotability.  I have been exploring questions related to pivotal variables (“Differences that Make a Difference” or “Difference In ⟹ Difference Out”) via logical analogues … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Computational Complexity, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Graph Theory, Hill Climbing, Hologrammautomaton, Logic, Logical Graphs, Logical Influence, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Pivotal Variables, Propositional Calculus, Propositional Equation Reasoning Systems, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Peirce’s 1903 Lowell Lectures • Comment 10

Posted on December 16, 2017 by Jon Awbrey

Re: Peirce List Discussion • John Sowa JFS: In the Lowell Lectures [1903] Peirce defined the Sheet of Assertion as the representation of a universe that was constructed during a discourse between Graphist and Grapheus. But that is just one … Continue reading →

Posted in C.S. Peirce, Diagrammatic Reasoning, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Peirce, Peirce List, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , | Leave a comment