Tag Archives: Mathematical Models

Differential Propositional Calculus • 3

Posted on February 24, 2020 by Jon Awbrey

Formal Development The preceding discussion outlined the ideas leading to the differential extension of propositional logic.  The next task is to lay out the concepts and terminology needed to describe various orders of differential propositional calculi. Elementary Notions Logical description … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Propositional Calculus • 2

Posted on February 22, 2020 by Jon Awbrey

Cactus Calculus Table 6 outlines a syntax for propositional calculus based on two types of logical connectives, both of variable -ary scope. A bracketed sequence of propositional expressions is taken to mean exactly one of the propositions is false, in … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Propositional Calculus • 1

Posted on February 18, 2020 by Jon Awbrey

A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Differential Propositional Calculus • Overview

Posted on February 16, 2020 by Jon Awbrey

The most fundamental concept in cybernetics is that of “difference”, either that two things are recognisably different or that one thing has changed with time. W. Ross Ashby • An Introduction to Cybernetics Here’s the outline of a sketch I … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Differential Logic and Dynamic Systems • Overview

Posted on September 10, 2019 by Jon Awbrey

In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade‑off between dynamic paradigms and symbolic paradigms.  Dynamic models take their cue from physics, using … Continue reading →

Posted in Amphecks, Boolean Functions, C.S. Peirce, Cactus Graphs, Category Theory, Change, Computational Complexity, Cybernetics, Differential Analytic Turing Automata, Differential Calculus, Differential Logic, Discrete Dynamics, Dynamical Systems, Equational Inference, Functional Logic, Gradient Descent, Graph Theory, Group Theory, Hologrammautomaton, Indicator Functions, Logic, Logical Graphs, Mathematical Models, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Time, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Where Is Fancy Bred? • Comment 1

Posted on September 14, 2018 by Jon Awbrey

Re: Artem Kaznatcheev • Labyrinth : Fitness Landscapes As Mazes, Not Mountains A species in progress, with its naturally evolved organs of sensitivity, effectivity, and discernment, in its trials to learn the properties of its environment, cannot be expected to … Continue reading →

Posted in Adaptive Systems, Analogy, Artem Kaznatcheev, Artificial Intelligence, Biological Systems, Communication, Computational Complexity, Control, Evolution, Fitness Landscapes, Imagination, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Mathematical Models, Mental Models, Natural Intelligence, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , | Leave a comment

Continuity, Generality, Infinity, Law, Synechism • 1

Posted on November 9, 2014 by Jon Awbrey

The concept of continuity Peirce highlights in his synechism is a logical principle somewhat more general than the concepts of either mathematical or physical continua. Peirce’s concept of continuity is better understood as a concept of lawful regularity or parametric … Continue reading →

Posted in Abduction, Aristotle, C.S. Peirce, Cardinality, Constraint, Continua, Continuity, Discreteness, Discretion, Epistemology, Generality, Infinity, Knowledge, Logic, Logic of Science, Mathematical Models, Mathematics, Natural Law, Physics, Quanta, Quantum Mechanics, Synechism, Topology | Tagged , , , , , , , , , , , , , , , , , , , , , , | 10 Comments

Objects, Models, Theories : 4

Posted on November 27, 2013 by Jon Awbrey

I need to stay with this problem a while … What are objects, models, theories, and how do they relate to one another? In contemplating this problem I always find it helpful to ruminate on the diagram shown above — … Continue reading →

Posted in Adaptive Systems, Analogy, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Information Theory, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Paradigms, Peirce, Pragmata, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 2 Comments

Objects, Models, Theories : 3

Posted on November 21, 2013 by Jon Awbrey

Re: Peirce List Discussion • Tom Gollier Here my task is to build bridges between several different classical and contemporary uses of the word model, so I don’t have the luxury of complete control over the words in play but … Continue reading →

Posted in Adaptive Systems, Analogy, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Peirce, Pragmata, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Objects, Models, Theories : 2

Posted on November 20, 2013 by Jon Awbrey

Re: K.W. Regan • The Graph Of Math Re: Artem Kaznatcheev • Three Types Of Mathematical Models What — if anything — is the common sense that connects the different senses of the word model, as it has been used … Continue reading →

Posted in Adaptive Systems, Analogy, Aristotle, Artificial Intelligence, Biological Systems, C.S. Peirce, Computational Complexity, Evolution, Gödel, Information, Inquiry, Inquiry Driven Systems, Learning Theory, Logic, Logic of Science, Mathematical Models, Mental Models, Model Theory, Natural Intelligence, Peirce, Pragmata, Semiotics | Tagged , , , , , , , , , , , , , , , , , , , , , | 8 Comments