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Jon AwbreySurvey of Differential Logic • 7 • <a href="https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/</a>This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.Please follow the above link for the full set of resources. Articles and blog series on the core ideas are linked below.Differential Logic • The Logic of Change and Difference • <a href="https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/</a>Differential Propositional Calculus • <a href="https://inquiryintoinquiry.com/2023/11/12/differential-propositional-calculus-overview-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/11/12/differential-propositional-calculus-overview-a/</a> • <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview</a>Differential Logic • <a href="https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/</a> • <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview</a>Differential Logic and Dynamic Systems • <a href="https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-a/</a> • <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview</a><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="tag">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="tag">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativePhysics" class="mention hashtag" rel="tag">#QualitativePhysics</a> <a href="https://mathstodon.xyz/tags/CactusCalculus" class="mention hashtag" rel="tag">#CactusCalculus</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="tag">#NeuralNetworkSystems</a> <a href="https://mathstodon.xyz/tags/CalculusOfLogicalDifferences" class="mention hashtag" rel="tag">#CalculusOfLogicalDifferences</a>

Jon AwbreySurvey of Differential Logic • 6 • <a href="https://inquiryintoinquiry.com/2023/11/10/survey-of-differential-logic-6/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/11/10/survey-of-differential-logic-6/</a>This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.Please follow the above link for the full set of resources. Articles and blog series on the core ideas are linked below.Differential Logic • The Logic of Change and Difference • <a href="https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/08/22/differential-logic-the-logic-of-change-and-difference/</a>Differential Propositional Calculus • <a href="https://inquiryintoinquiry.com/2023/11/12/differential-propositional-calculus-overview-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/11/12/differential-propositional-calculus-overview-a/</a>Differential Logic • <a href="https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/</a>Differential Logic and Dynamic Systems • <a href="https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-a/</a>cc: <a href="https://www.academia.edu/community/lQX66L" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://www.academia.edu/community/lQX66L</a><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="tag">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="tag">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativePhysics" class="mention hashtag" rel="tag">#QualitativePhysics</a> <a href="https://mathstodon.xyz/tags/CactusCalculus" class="mention hashtag" rel="tag">#CactusCalculus</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="tag">#NeuralNetworkSystems</a> <a href="https://mathstodon.xyz/tags/CalculusOfLogicalDifferences" class="mention hashtag" rel="tag">#CalculusOfLogicalDifferences</a>

Jon AwbreyDifferential Logic • The Logic of Change and Difference • <a href="https://inquiryintoinquiry.com/2023/08/22/differential-logic-%ce%b1/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/08/22/differential-logic-%ce%b1/</a>Differential logic is the logic of variation — the logic of change and difference.Differential logic is the component of logic whose object is the description of variation, for example, the aspects of change, difference, distribution, and diversity, in universes of discourse subject to qualitative logical description. In its formalization, differential logic treats the principles governing the use of a “differential logical calculus”, in other words, a formal system with the expressive capacity to describe change and diversity in logical universes of discourse.A simple case of a differential logical calculus is furnished by a differential propositional calculus. This augments ordinary propositional calculus in the same way the differential calculus of Leibniz and Newton augments the analytic geometry of Descartes.Resources —Differential Logic • <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview</a> • Part 1 ( <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1</a> ) • Part 2 ( <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2</a> ) • Part 3 ( <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3</a> )Differential Propositional Calculus • <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview</a> • Part 1 ( <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1</a> ) • Part 2 ( <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2</a> )Differential Logic and Dynamic Systems • <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview</a> • Part 1 ( <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1</a> ) • Part 2 ( <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2</a> ) • Part 3 ( <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3</a> ) • Part 4 ( <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4</a> ) • Part 5 ( <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5</a> )<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DiscreteDynamicalSystems" class="mention hashtag" rel="tag">#DiscreteDynamicalSystems</a> <a href="https://mathstodon.xyz/tags/Leibniz" class="mention hashtag" rel="tag">#Leibniz</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="tag">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativeDynamics" class="mention hashtag" rel="tag">#QualitativeDynamics</a> <a href="https://mathstodon.xyz/tags/DifferentialPropositions" class="mention hashtag" rel="tag">#DifferentialPropositions</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="tag">#NeuralNetworkSystems</a>

Jon AwbreySurvey of Differential Logic • 5 • <a href="https://inquiryintoinquiry.com/2023/04/25/survey-of-differential-logic-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/04/25/survey-of-differential-logic-5/</a>This is a Survey of work in progress on Differential Logic, resources under development toward a more systematic treatment.Differential logic is the component of logic whose object is the description of variation — the aspects of change, difference, distribution, and diversity — in universes of discourse subject to logical description. A definition as broad as that naturally incorporates any study of variation by way of mathematical models, but differential logic is especially charged with the qualitative aspects of variation pervading or preceding quantitative models. To the extent a logical inquiry makes use of a formal system, its differential component treats the use of a differential logical calculus — a formal system with the expressive capacity to describe change and diversity in logical universes of discourse. Please follow the above link for the full set of resources. Articles and blog series on the core ideas are linked below.Differential Propositional Calculus • <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Overview</a> 1 <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_1</a> 2 <a href="https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Propositional_Calculus_%E2%80%A2_Part_2</a> • <a href="https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2020/02/16/differential-propositional-calculus-overview/</a>Differential Logic • <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Overview</a> 1 <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_1</a> 2 <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_2</a> 3 <a href="https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_%E2%80%A2_Part_3</a> • <a href="https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2020/03/20/differential-logic-overview/</a>Differential Logic and Dynamic Systems • <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview</a> 1 <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1</a> 2 <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_2</a> 3 <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_3</a> 4 <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_4</a> 5 <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_5</a> • <a href="https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/</a><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="tag">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="tag">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativePhysics" class="mention hashtag" rel="tag">#QualitativePhysics</a> <a href="https://mathstodon.xyz/tags/CactusCalculus" class="mention hashtag" rel="tag">#CactusCalculus</a> <a 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Jon AwbreyDifferential Logic and Dynamic Systems • Review and Transition 1 • <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1#Review_and_Transition" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part_1#Review_and_Transition</a>This note continues a previous discussion on the problem of dealing with change and diversity in logic-based intelligent systems. It is useful to begin by summarizing essential material from previous reports.Table 1 outlines a notation for propositional calculus based on two types of logical connectives, both of variable \(k\)-ary scope.• A bracketed list of propositional expressions in the form \(\texttt{(} e_1 \texttt{,} e_2 \texttt{,} \ldots \texttt{,} e_{k-1} \texttt{,} e_k \texttt{)}\) indicates that exactly one of the propositions \(e_1, e_2, \ldots, e_{k-1}, e_k\) is false.• A concatenation of propositional expressions in the form \(e_1 ~ e_2 ~ \ldots ~ e_{k-1} ~ e_k\) indicates that all of the propositions \(e_1, e_2, \ldots, e_{k-1}, e_k\) are true, in other words, that their logical conjunction is true.All other propositional connectives can be obtained in a very efficient style of representation through combinations of these two forms. Strictly speaking, the concatenation form is dispensable in light of the bracketed form but it is convenient to maintain it as an abbreviation of more complicated bracket expressions.<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="tag">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="tag">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativeChange" class="mention hashtag" rel="tag">#QualitativeChange</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="tag">#NeuralNetworkSystems</a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#Semiotics</a>

Jon AwbreyDifferential Logic and Dynamic Systems • Overview • <a href="https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/03/04/differential-logic-and-dynamic-systems-overview-2/</a> • <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview</a>❝Stand and unfold yourself.❞ — Hamlet • Francisco • 1.1.2In 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 quantitative measures and differential equations to model the evolution of a system’s state through time. Symbolic models use logical methods to describe systems and their agents in qualitative terms, deriving logical consequences of a system’s description or an agent’s state of information. Logic-based systems have tended to be static in character, largely because we have lacked a proper logical analogue of differential calculus. The work laid out in this report is intended to address that lack.This article develops a differential extension of propositional calculus and applies it to the analysis of dynamic systems whose states are described in qualitative logical terms. The work pursued here is coordinated with a parallel application focusing on neural network systems but the dependencies are arranged to make the present article the main and the more self-contained work, to serve as a conceptual frame and a technical background for the network project.<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="tag">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="tag">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativeChange" class="mention hashtag" rel="tag">#QualitativeChange</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="tag">#NeuralNetworkSystems</a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#Semiotics</a>

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