#BooleanFunctions

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Jon AwbreyLogical Graphs • Discussion 5 • <a href="https://inquiryintoinquiry.com/2023/08/28/logical-graphs-discussion-5/" rel="nofollow noopener noreferrer" target="_blank">https://inquiryintoinquiry.com/2023/08/28/logical-graphs-discussion-5/</a>Re: Logical Graphs • First Impressions • <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" rel="nofollow noopener noreferrer" target="_blank">https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/</a> Re: Facebook • Daniel Everett • <a href="https://www.facebook.com/permalink.php?story_fbid=pfbid026jD3t75k69Wbs9q3qaCAvTA6zb1GXCqwu4ZWfssxgGGd1er7Wwz8PyygiQUmF6t3l&id=100093271525294" rel="nofollow noopener noreferrer" target="_blank">https://www.facebook.com/permalink.php?story_fbid=pfbid026jD3t75k69Wbs9q3qaCAvTA6zb1GXCqwu4ZWfssxgGGd1er7Wwz8PyygiQUmF6t3l&id=100093271525294</a>DE: Nice discussion. Development of icon-based reasoning.My Comment —As it happens, even though Peirce's systems of logical graphs do have iconic features, their real power over other sorts of logical diagrams (like venn diagrams) is due to their deeper symbolic character. Thereby will hang many tales to come …<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EntitativeGraphs</a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ExistentialGraphs</a> <a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SpencerBrown</a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LawsOfForm</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PropositionalCalculus</a>

Jon AwbreyLogical Graphs • First Impressions 1 • <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" rel="nofollow noopener noreferrer" target="_blank">https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/</a>Introduction • Moving Pictures of Thought —A “logical graph” is a graph-theoretic structure in one of the systems of graphical syntax Charles Sanders Peirce developed for logic.In numerous papers on “qualitative logic”, “entitative graphs”, and “existential graphs”, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.In the century since Peirce initiated this line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph-theoretic structures. This article examines the common basis of these formal systems from a bird's eye view, focusing on the aspects of form shared by the entire family of algebras, calculi, or languages, however they happen to be viewed in a given application.<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EntitativeGraphs</a> <a href="https://mathstodon.xyz/tags/ExistensialGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ExistensialGraphs</a> <a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SpencerBrown</a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LawsOfForm</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PropositionalCalculus</a>

Jon AwbreyDifferential Logic • <a href="https://inquiryintoinquiry.com/2023/08/22/differential-logic-%ce%b1/" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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" rel="nofollow noopener noreferrer" target="_blank">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="nofollow noopener noreferrer" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DiscreteDynamicalSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DiscreteDynamicalSystems</a> <a href="https://mathstodon.xyz/tags/Leibniz" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Leibniz</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativeDynamics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QualitativeDynamics</a> <a href="https://mathstodon.xyz/tags/DifferentialPropositions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialPropositions</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NeuralNetworkSystems</a>

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" rel="nofollow noopener noreferrer" target="_blank">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="nofollow noopener noreferrer" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativeChange" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QualitativeChange</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NeuralNetworkSystems</a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Semiotics</a>

Jon AwbreyDifferential Logic and Dynamic Systems • Overview • <a href="https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview" rel="nofollow noopener noreferrer" target="_blank">https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Overview</a>❝Stand and unfold yourself.❞ — Hamlet • Francisco • 1.1.2This 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="nofollow noopener noreferrer" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/DynamicSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DynamicSystems</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/BooleanDifferenceCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanDifferenceCalculus</a> <a href="https://mathstodon.xyz/tags/QualitativeChange" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QualitativeChange</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#MinimalNegationOperators</a> <a href="https://mathstodon.xyz/tags/NeuralNetworkSystems" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NeuralNetworkSystems</a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Semiotics</a>

Jon Awbrey<a href="https://mathstodon.xyz/@bblfish" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@bblfish</a> <a href="https://fosstodon.org/@josd" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@josd</a> <a href="https://social.logilab.org/@semwebpro" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@semwebpro</a> <a href="https://scholar.social/@hochstenbach" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@hochstenbach</a> One thing I found out early on is how critical it is to get <a href="https://mathstodon.xyz/tags/AlphaGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AlphaGraphs</a> (<a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a>, <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PropositionalCalculus</a>, <a href="https://mathstodon.xyz/tags/ZerothOrderLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ZerothOrderLogic</a>) down tight. If you do that it changes how you view <a href="https://mathstodon.xyz/tags/FOL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FOL</a> (<a href="https://mathstodon.xyz/tags/PredicateCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PredicateCalculus</a>, <a href="https://mathstodon.xyz/tags/QuantificationalLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#QuantificationalLogic</a>). That tends to rub people who view FOL as <a href="https://mathstodon.xyz/tags/GOL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GOL</a> (<a href="https://mathstodon.xyz/tags/GodsOwnLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GodsOwnLogic</a>) the wrong way so you have watch out for that if you go down this road.Here's a primer on \(\alpha\) <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> as I see them — • <a href="https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no" rel="nofollow noopener noreferrer" target="_blank">https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no</a>

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#BooleanFunctions