Jon Awbrey<p>Logical Graphs • Formal Development 1<br />• <a href="https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-1-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/09</span><span class="invisible">/12/logical-graphs-formal-development-1-a/</span></a></p><p>Recap —</p><p>A first approach to logical graphs was outlined in the article linked below.</p><p>Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/08</span><span class="invisible">/26/logical-graphs-first-impressions-a/</span></a></p><p>That introduced the initial elements of logical graphs and hopefully supplied the reader with an intuitive sense of their motivation and rationale.</p><p>Formal Development —</p><p>Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner.</p><p>The next order of business is to give the precise axioms used to develop the formal system of logical graphs. The axioms derive from C.S. Peirce's various systems of graphical syntax via the “calculus of indications” described in Spencer Brown's “Laws of Form”. The formal proofs to follow will use a variation of Spencer Brown's annotation scheme to mark each step of the proof according to which axiom is called to license the corresponding step of syntactic transformation, whether it applies to graphs or to strings.</p><p>Resources —</p><p>Survey of Animated Logical Graphs<br />• <a href="https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/18/survey-of-animated-logical-graphs-7/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
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Jon Awbrey<p>Logical Graphs • First Impressions 1<br />• <a href="https://inquiryintoinquiry.com/2024/08/30/logical-graphs-first-impressions-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/08</span><span class="invisible">/30/logical-graphs-first-impressions-1/</span></a></p><p>Moving Pictures of Thought —</p><p>A logical graph is a graph‑theoretic structure in one of the systems of graphical syntax Charles S. Peirce developed for logic.</p><p>Introduction —</p><p>In numerous papers on qualitative logic, entitative graphs, and existential graphs, C.S. Peirce developed several versions of a graphical formalism, or a graph‑theoretic formal language, designed to be interpreted for logic.</p><p>In the century since Peirce initiated their line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph‑theoretic structures. The posts to follow explore the common basis of those 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.</p><p>Resources —</p><p>Logical Graphs<br />• <a href="https://oeis.org/wiki/Logical_Graphs" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Logical_Graphs</span><span class="invisible"></span></a></p><p>Futures Of Logical Graphs<br />• <a href="https://oeis.org/wiki/Futures_Of_Logical_Graphs" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Futures_Of_Logic</span><span class="invisible">al_Graphs</span></a></p><p>Propositional Equation Reasoning Systems<br />• <a href="https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Propositional_Eq</span><span class="invisible">uation_Reasoning_Systems</span></a></p><p>Charles Sanders Peirce • Bibliography<br />• <a href="https://mywikibiz.com/Charles_Sanders_Peirce" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mywikibiz.com/Charles_Sanders_</span><span class="invisible">Peirce</span></a><br />• <a href="https://mywikibiz.com/Charles_Sanders_Peirce_%28Bibliography%29" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">mywikibiz.com/Charles_Sanders_</span><span class="invisible">Peirce_%28Bibliography%29</span></a> </p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Transformations of Logical Graphs • Discussion 1<br />• <a href="https://inquiryintoinquiry.com/2024/05/22/transformations-of-logical-graphs-discussion-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/22/transformations-of-logical-graphs-discussion-1/</span></a></p><p>Re: Laws of Form<br />• <a href="https://groups.io/g/lawsofform/topic/transformations_of_logical/105927945" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">groups.io/g/lawsofform/topic/t</span><span class="invisible">ransformations_of_logical/105927945</span></a></p><p>Mauro Bertani<br />• <a href="https://groups.io/g/lawsofform/message/3204" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">groups.io/g/lawsofform/message</span><span class="invisible">/3204</span></a></p><p>Dear Mauro,</p><p>The couple of pages linked below give the clearest and quickest introduction I've been able to manage so far when it comes to the elements of logical graphs, at least, in the way I've come to understand them. The first page gives a lot of detail by way of motivation and computational implementation, so you could easily put that off till you feel a need for it. The second page lays out the precise axioms or initials I use — the first algebraic axiom varies a bit from Spencer Brown for a better fit with C.S. Peirce — and also shows the parallels between the dual interpretations.</p><p>Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/01/logical-graphs-formal-development-a/</span></a></p><p>Additional Resources —</p><p>Logic Syllabus<br />• <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/logic-s</span><span class="invisible">yllabus/</span></a></p><p>Survey of Animated Logical Graphs<br />• <a href="https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/18/survey-of-animated-logical-graphs-7/</span></a></p><p>Survey of Semiotics, Semiosis, Sign Relations<br />• <a href="https://inquiryintoinquiry.com/2024/01/26/survey-of-semiotics-semiosis-sign-relations-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/01</span><span class="invisible">/26/survey-of-semiotics-semiosis-sign-relations-5/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/MathematicalDuality" class="mention hashtag" rel="tag">#<span>MathematicalDuality</span></a> <a href="https://mathstodon.xyz/tags/Form" class="mention hashtag" rel="tag">#<span>Form</span></a></p>
Jon Awbrey<p>Mathematical Duality in Logical Graphs • Discussion 2.2<br />• <a href="https://inquiryintoinquiry.com/2024/05/04/mathematical-duality-in-logical-graphs-discussion-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/04/mathematical-duality-in-logical-graphs-discussion-2/</span></a></p><p>What you say about deriving arithmetic, algebra, group theory, and all the rest from the calculus of indications may well be true, but it remains to be shown if so, and that's aways down the road from here.</p><p>Resources —</p><p>Logic Syllabus<br />• <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/logic-s</span><span class="invisible">yllabus/</span></a></p><p>Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/01/logical-graphs-formal-development-a/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/MathematicalDuality" class="mention hashtag" rel="tag">#<span>MathematicalDuality</span></a> <a href="https://mathstodon.xyz/tags/Form" class="mention hashtag" rel="tag">#<span>Form</span></a></p>
Jon Awbrey<p>Mathematical Duality in Logical Graphs • Discussion 1<br />• <a href="https://inquiryintoinquiry.com/2024/05/04/mathematical-duality-in-logical-graphs-discussion-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/04/mathematical-duality-in-logical-graphs-discussion-1/</span></a></p><p>Re: Mathematical Duality in Logical Graphs • 1<br />• <a href="https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/03/mathematical-duality-in-logical-graphs-1/</span></a></p><p>Re: Laws of Form • Lyle Anderson<br />• <a href="https://groups.io/g/lawsofform/message/109" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">groups.io/g/lawsofform/message</span><span class="invisible">/109</span></a></p><p>Re: Brading, K., Castellani, E., and Teh, N., (2017), “Symmetry and Symmetry Breaking”, The Stanford Encyclopedia of Philosophy (Winter 2017), Edward N. Zalta (ed.).<br />• <a href="https://plato.stanford.edu/archives/win2017/entries/symmetry-breaking/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">plato.stanford.edu/archives/wi</span><span class="invisible">n2017/entries/symmetry-breaking/</span></a></p><p>Dear Lyle,</p><p>Thanks for the link to the article on symmetry and symmetry breaking. I did once take a Master's in Mathematics, specializing in combinatorics, graph theory, and group theory. When it comes to the bearing of symmetry groups on logical graphs and the calculus of indications, it will take careful attention to the details of the relationship between the two interpretations singled out by Peirce and Spencer Brown.</p><p>Both Peirce and Spencer Brown recognized the relevant duality, if they differed in what they found most convenient to use in their development and exposition, and most of us will emphasize one interpretation or the other as a matter of facility or taste in a chosen application, so it requires a bit of effort to keep the underlying unity in focus. I recently made another try at taking a more balanced view, drawing up a series of tables in parallel columns the way one commonly does with dual theorems in projective geometry, so I will shortly share more of that work.</p><p>Resources —</p><p>Logic Syllabus<br />• <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/logic-s</span><span class="invisible">yllabus/</span></a></p><p>Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/01/logical-graphs-formal-development-a/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Mathematical Duality in Logical Graphs • 1.2<br />• <a href="https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/03/mathematical-duality-in-logical-graphs-1/</span></a></p><p>It was in this context that Peirce's systems of logical graphs developed, issuing in dual interpretations of the same formal axioms which Peirce referred to as “entitative graphs” and “existential graphs”, respectively. He developed only the existential interpretation to any great extent, since the extension from propositional to relational calculus appeared more natural in that case, but whether there is any logical or mathematical reason for the symmetry to break at that point is a good question for further research.</p><p>Resources —</p><p>Duality Indicating Unity<br />• <a href="https://inquiryintoinquiry.com/2013/01/31/duality-indicating-unity-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2013/01</span><span class="invisible">/31/duality-indicating-unity-1/</span></a></p><p>C.S. Peirce • Logic of Number<br />• <a href="https://inquiryintoinquiry.com/2012/09/01/c-s-peirce-logic-of-number-ms-229/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2012/09</span><span class="invisible">/01/c-s-peirce-logic-of-number-ms-229/</span></a></p><p>C.S. Peirce • Syllabus • Selection 1<br />• <a href="https://inquiryintoinquiry.com/2014/08/24/c-s-peirce-syllabus-selection-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2014/08</span><span class="invisible">/24/c-s-peirce-syllabus-selection-1/</span></a></p><p>References —</p><p>• Peirce, C.S., [Logic of Number — Le Fevre] (MS 229), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 2, 592–595.</p><p>• Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, UK.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/MathematicalDuality" class="mention hashtag" rel="tag">#<span>MathematicalDuality</span></a> <a href="https://mathstodon.xyz/tags/Form" class="mention hashtag" rel="tag">#<span>Form</span></a></p>
Jon Awbrey<p>Mathematical Duality in Logical Graphs • 1.1<br />• <a href="https://inquiryintoinquiry.com/2024/05/03/mathematical-duality-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/05</span><span class="invisible">/03/mathematical-duality-in-logical-graphs-1/</span></a></p><p>“All other sciences without exception depend upon the principles of mathematics; and mathematics borrows nothing from them but hints.”</p><p>— C.S. Peirce • “Logic of Number”</p><p>“A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re‑align them with mathematics.”</p><p>— G. Spencer Brown • “Laws of Form”</p><p>The duality between entitative and existential interpretations of logical graphs tells us something important about the relation between logic and mathematics. It tells us the mathematical forms giving structure to reasoning are deeper and more abstract at once than their logical interpretations.</p><p>A formal duality points to a more encompassing unity, founding a calculus of forms whose expressions can be read in alternate ways by switching the meanings assigned to a pair of primitive terms. Spencer Brown's mathematical approach to “Laws of Form” and the whole of Peirce's work on the mathematics of logic shows both thinkers were deeply aware of this principle.</p><p>Peirce explored a variety of dualities in logic which he treated on analogy with the dualities in projective geometry. This gave rise to formal systems where the initial constants, and thus their geometric and graph‑theoretic representations, had no uniquely fixed meanings but could be given dual interpretations in logic.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/MathematicalDuality" class="mention hashtag" rel="tag">#<span>MathematicalDuality</span></a> <a href="https://mathstodon.xyz/tags/Form" class="mention hashtag" rel="tag">#<span>Form</span></a></p>
Jon Awbrey<p>Operator Variables in Logical Graphs • Discussion 2<br />• <a href="https://inquiryintoinquiry.com/2024/04/09/operator-variables-in-logical-graphs-discussion-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/04</span><span class="invisible">/09/operator-variables-in-logical-graphs-discussion-2/</span></a></p><p>Re: Operator Variables in Logical Graphs • 1<br />• <a href="https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/04</span><span class="invisible">/06/operator-variables-in-logical-graphs-1/</span></a></p><p>Re: Cybernetics List • Lou Kauffman<br />• <a href="https://groups.google.com/g/cybcom/c/XKT76QI_OnI/m/3u9P2Ir5AgAJ" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">groups.google.com/g/cybcom/c/X</span><span class="invisible">KT76QI_OnI/m/3u9P2Ir5AgAJ</span></a></p><p>LK:<br />❝I am writing to comment that there are some quite interesting situations that generalize the DeMorgan Duality.</p><p>❝One well-known one is this. Let R* denote the real numbers with a formal symbol @, denoting infinity, adjoined so that:</p><p>• @ + @ = @<br />• @ + 0 = @<br />• @ + x = @ when x is an ordinary real number<br />• 1 ÷ @ = 0</p><p>❝(Of course you cannot do anything with @ or the system collapses. One can easily give the constraints.)</p><p>❝Define ¬x = 1/x.</p><p>• x + y = usual sum otherwise.</p><p>❝Define x ∗ y = xy/(x + y) = 1/((1/x) + (1/y)).</p><p>❝Then we have x ∗ y = ¬(¬x + ¬y), so that the system (R*, ¬, +, ∗) satisfies DeMorgan duality and it is a Boolean algebra when restricted to {0, @}.</p><p>❝Note also that ¬ fixes 1 and -1. This algebraic system occurs of course in electrical calculations and also in the properties of tangles in knot theory, as you can read in the last part of my included paper “Knot Logic”. I expect there is quite a bit more about this kind of duality in various (categorical) places.❞</p><p>Thanks, Lou, there's a lot to think about here, so I'll need to study it a while. Just off hand, the embedding into reals brings up a vague memory of the very curious way Peirce defines negation in his 1870 “Logic of Relatives”. I seem to recall it involving a power series, but it's been a while so I'll have to look it up again.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Operator Variables in Logical Graphs • Discussion 1<br />• <a href="https://inquiryintoinquiry.com/2024/04/08/operator-variables-in-logical-graphs-discussion-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/04</span><span class="invisible">/08/operator-variables-in-logical-graphs-discussion-1/</span></a></p><p>Re: Operator Variables in Logical Graphs • 1<br />• <a href="https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/04</span><span class="invisible">/06/operator-variables-in-logical-graphs-1/</span></a></p><p>Re: Academia.edu • Stephen Duplantier<br />• <a href="https://www.academia.edu/community/Lxn1Ww?c=yq1Rxy" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/community/Lxn1Ww?</span><span class="invisible">c=yq1Rxy</span></a></p><p>SD: <br />❝The best way for me to read Peirce is as if he was writing poetry. So if his algebra is poetry — I imagine him approving of the approach since he taught me abduction in the first place — there is room to wander. With this, I venture the idea that his “wide field” is a local algebraic geography far from the tended garden. There, where weeds and wild things grow and hybridize are the non‑dichotomic mathematics.❞</p><p>Stephen,</p><p>“Abdeuces Are Wild”, as they say, maybe not today, maybe not tomorrow, but soon …</p><p>As far as my own guess, and a lot of my wandering in pursuit of it goes, I'd venture Peirce's field of vision opens up not so much from dichotomic to trichotomic domains of value as from dyadic to triadic relations, and all that with particular significance into the medium of reflection afforded by triadic sign relations.</p><p>Resources —</p><p>Logic Syllabus<br />• <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/logic-s</span><span class="invisible">yllabus/</span></a></p><p>Semeiotic<br />• <a href="https://oeis.org/wiki/Semeiotic" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Semeiotic</span><span class="invisible"></span></a></p><p>Sign Relations<br />• <a href="https://oeis.org/wiki/Sign_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Sign_relation</span><span class="invisible"></span></a></p><p>Triadic Relations<br />• <a href="https://oeis.org/wiki/Triadic_relation" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Triadic_relation</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/LogicalOperatorVariables" class="mention hashtag" rel="tag">#<span>LogicalOperatorVariables</span></a></p>
Jon Awbrey<p>Operator Variables in Logical Graphs • 1.2<br />• <a href="https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/04</span><span class="invisible">/06/operator-variables-in-logical-graphs-1/</span></a></p><p>Consider De Morgan's rules:</p><p>• ¬(A ∧ B) = ¬A ∨ ¬B </p><p>• ¬(A ∨ B) = ¬A ∧ ¬B</p><p>The common form exhibited by the two rules could be captured in a single formula by taking “o₁” and “o₂” as variable names ranging over a family of logical operators, then asking what substitutions for o₁ and o₂ would satisfy the following equation.</p><p>• ¬(A o₁ B) = ¬A o₂ ¬B</p><p>We already know two solutions to this “operator equation”, namely, (o₁, o₂) = (∧, ∨) and (o₁, o₂) = (∨, ∧). Wouldn't it be just like Peirce to ask if there are others?</p><p>Having broached the subject of “logical operator variables”, I will leave it for now in the same way Peirce himself did:</p><p>❝I shall not further enlarge upon this matter at this point, although the conception mentioned opens a wide field; because it cannot be set in its proper light without overstepping the limits of dichotomic mathematics.❞ (Peirce, CP 4.306).</p><p>Further exploration of operator variables and operator invariants treads on grounds traditionally known as second intentional logic and “opens a wide field”, as Peirce says. For now, however, I will tend to that corner of the field where our garden variety logical graphs grow, observing the ways in which operative variations and operative themes naturally develop on those grounds.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/LogicalOperatorVariables" class="mention hashtag" rel="tag">#<span>LogicalOperatorVariables</span></a></p>
Jon Awbrey<p>Operator Variables in Logical Graphs • 1.1<br />• <a href="https://inquiryintoinquiry.com/2024/04/06/operator-variables-in-logical-graphs-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/04</span><span class="invisible">/06/operator-variables-in-logical-graphs-1/</span></a></p><p>In lieu of a field study requirement for my bachelor's degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan State had at the time, all in trying to track down some hint of a clue to a puzzling passage in Peirce's “Simplest Mathematics”, most acutely coming to a head with that bizarre line of type at CP 4.306, which the editors of Peirce's “Collected Papers”, no doubt compromised by the typographer's reluctance to cut new symbols, transmogrified into a script more cryptic than even the manuscript's original hieroglyphic.</p><p>I found one key to the mystery in Peirce's use of “operator variables”, which he and his students Christine Ladd‑Franklin and O.H. Mitchell explored in depth. I will shortly discuss that theme as it affects logical graphs but it may be useful to give a shorter and sweeter explanation of how the basic idea typically arises in common logical practice.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperators" class="mention hashtag" rel="tag">#<span>MinimalNegationOperators</span></a> <a href="https://mathstodon.xyz/tags/LogicalOperatorVariables" class="mention hashtag" rel="tag">#<span>LogicalOperatorVariables</span></a></p>
Jon Awbrey<p>Survey of Animated Logical Graphs • 7<br />• <a href="https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/03</span><span class="invisible">/18/survey-of-animated-logical-graphs-7/</span></a></p><p>This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph‑theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.</p><p>Please follow the above link for the full set of resources.<br />Articles and blog series on the core ideas are linked below.</p><p>Beginnings —</p><p>Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/01/logical-graphs-formal-development-a/</span></a></p><p>Elements —</p><p>Logic Syllabus<br />• <a href="https://oeis.org/wiki/Logic_Syllabus" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Logic_Syllabus</span><span class="invisible"></span></a></p><p>Logical Graphs<br />• <a href="https://oeis.org/wiki/Logical_Graphs" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Logical_Graphs</span><span class="invisible"></span></a></p><p>Minimal Negation Operators<br />• <a href="https://oeis.org/wiki/Minimal_negation_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Minimal_negation</span><span class="invisible">_operator</span></a></p><p>Propositional Equation Reasoning Systems<br />• <a href="https://oeis.org/wiki/Propositional_Equation_Reasoning_Systems" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Propositional_Eq</span><span class="invisible">uation_Reasoning_Systems</span></a></p><p>Examples —</p><p>Peirce's Law<br />• <a href="https://inquiryintoinquiry.com/2023/10/18/peirces-law-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/10</span><span class="invisible">/18/peirces-law-a/</span></a><br />• <a href="https://oeis.org/wiki/Peirce%27s_law" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="">oeis.org/wiki/Peirce%27s_law</span><span class="invisible"></span></a></p><p>Praeclarum Theorema<br />• <a href="https://inquiryintoinquiry.com/2023/10/05/praeclarum-theorema-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/10</span><span class="invisible">/05/praeclarum-theorema-a/</span></a><br />• <a href="https://oeis.org/wiki/Logical_Graphs#Praeclarum_theorema" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Logical_Graphs#P</span><span class="invisible">raeclarum_theorema</span></a> </p><p>Proof Animations<br />• <a href="https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/User:Jon_Awbrey/</span><span class="invisible">ANIMATION#Proof_Animations</span></a></p><p>Excursions —</p><p>Cactus Language<br />• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Overview</span></a></p><p>Futures Of Logical Graphs<br />• <a href="https://oeis.org/wiki/Futures_Of_Logical_Graphs" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Futures_Of_Logic</span><span class="invisible">al_Graphs</span></a></p><p>Applications —</p><p>Applications of a Propositional Calculator • Constraint Satisfaction Problems<br />• <a href="https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator_Constraint_Satisfaction_Problems" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/4727842/Applicati</span><span class="invisible">ons_of_a_Propositional_Calculator_Constraint_Satisfaction_Problems</span></a> </p><p>Exploratory Qualitative Analysis of Sequential Observation Data<br />• <a href="https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/User:Jon_Awbrey/</span><span class="invisible">Exploratory_Qualitative_Analysis_of_Sequential_Observation_Data</span></a></p><p>Differential Analytic Turing Automata<br />• <a href="https://oeis.org/wiki/Differential_Analytic_Turing_Automata_%E2%80%A2_Overview" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Differential_Ana</span><span class="invisible">lytic_Turing_Automata_%E2%80%A2_Overview</span></a></p><p>Survey of Theme One Program<br />• <a href="https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/02</span><span class="invisible">/26/survey-of-theme-one-program-6/</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a> <br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <br /><a href="https://mathstodon.xyz/tags/CactusSyntax" class="mention hashtag" rel="tag">#<span>CactusSyntax</span></a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperator" class="mention hashtag" rel="tag">#<span>MinimalNegationOperator</span></a> <a href="https://mathstodon.xyz/tags/PeircesLaw" class="mention hashtag" rel="tag">#<span>PeircesLaw</span></a> <a href="https://mathstodon.xyz/tags/TuringAutomata" class="mention hashtag" rel="tag">#<span>TuringAutomata</span></a></p>
Jon Awbrey<p>Logical Graphs • Discussion 9<br />• <a href="http://inquiryintoinquiry.com/2023/10/12/logical-graphs-discussion-9/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">http://</span><span class="ellipsis">inquiryintoinquiry.com/2023/10</span><span class="invisible">/12/logical-graphs-discussion-9/</span></a></p><p>Re: Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-a/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/01/logical-graphs-formal-development-a/</span></a><br />Re: Laws of Form • Lyle Anderson<br />• <a href="https://groups.io/g/lawsofform/message/2511" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">groups.io/g/lawsofform/message</span><span class="invisible">/2511</span></a></p><p>LA:<br />❝The Gestalt Switch from parenthesis to graphs is stimulating. There are probably things in Laws of Form that we didn't see because we were blinded by the crosses.❞</p><p>That has been my experience. Viewing a space of mathematical objects from a new angle and changing the basis of representation can bring out new and surprising aspects of their form and even expand the field of view to novel directions of generalization.</p><p>One of the first things I learned in the early years of computing with logical graphs is how essential it is to “slip the surly bonds” of the planar embedding and work with free trees in a space of their own.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Logical Graphs • Discussion 7<br />• <a href="https://inquiryintoinquiry.com/2023/10/01/logical-graphs-discussion-7/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/10</span><span class="invisible">/01/logical-graphs-discussion-7/</span></a></p><p>Re: Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2023/09/01/logical-graphs-formal-development-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/01/logical-graphs-formal-development-2/</span></a><br />Re: Laws of Form • Alex Shkotin<br />• <a href="https://groups.io/g/lawsofform/message/2461" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">groups.io/g/lawsofform/message</span><span class="invisible">/2461</span></a></p><p>AS:<br />❝When we look at undirected graph it is usual, before describing a rules of graph transformation, to describe exactly what kind of graphs we are working with ...❞</p><p>Hi Alex,</p><p>I am traveling this week, with limited internet. There's a quickie glossary under the heading “Painted And Rooted Cacti” on the following blog page.</p><p>Theme One Program • Exposition 2<br />• <a href="https://inquiryintoinquiry.com/2022/06/16/theme-one-program-exposition-2-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/06</span><span class="invisible">/16/theme-one-program-exposition-2-2/</span></a></p><p>Regards,<br />Jon</p><p>P.S. Back home now ... with access to books ... will attempt to fill in some of the blanks in last week's sketchy vacation messages. —JA</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Logical Graphs • Formal Development 1<br />• <a href="https://inquiryintoinquiry.com/2023/09/15/logical-graphs-formal-development-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/09</span><span class="invisible">/15/logical-graphs-formal-development-1/</span></a></p><p>Recap —</p><p>A first approach to logical graphs can be found in the article linked below.</p><p>Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>That introduces the initial elements of logical graphs and hopefully supplies the reader with an intuitive sense of their motivation and rationale.</p><p>Formal Development —</p><p>Logical graphs are next presented as a formal system by going back to the initial elements and developing their consequences in a systematic manner.</p><p>The next order of business is to give the precise axioms used to develop the formal system of logical graphs. The axioms derive from C.S. Peirce's various systems of graphical syntax via the “calculus of indications” described in Spencer Brown's “Laws of Form”. The formal proofs to follow will use a variation of Spencer Brown's annotation scheme to mark each step of the proof according to which axiom is called to license the corresponding step of syntactic transformation, whether it applies to graphs or to strings.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Logical Graphs • Discussion 6<br />• <a href="https://inquiryintoinquiry.com/2023/08/29/logical-graphs-discussion-6/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/29/logical-graphs-discussion-6/</span></a></p><p>Re: Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>Logical Graphs • Figures 1 and 2<br />• <a href="https://inquiryintoinquiry.files.wordpress.com/2023/08/logical-graph-figures-1-2-framed.png" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.files.wordp</span><span class="invisible">ress.com/2023/08/logical-graph-figures-1-2-framed.png</span></a></p><p>Re: Academia.edu • Robert Appleton<br />• <a href="https://www.academia.edu/community/lavbw5?c=Q4jlVy" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/community/lavbw5?</span><span class="invisible">c=Q4jlVy</span></a></p><p>RA:<br />❝As a professional graphic designer and non-mathematician reading your two diagrams, I need to ask for a simpler statement of their purpose. What do Fig 1 and Fig 2 represent to you? And what insight do they provide us?❞</p><p>My Comment —</p><p>Figures 1 and 2 are really just a couple of “in medias res” pump‑primers or ice‑breakers. This will all be explained in the above linked blog post, where I'm revising the text and upgrading the graphics of some work I first blogged in 2008 based on work I did even further back. I'll be taking a fresh look at that as I serialize it here.</p><p>Those two Figures come from George Spencer Brown's 1969 book Laws of Form, where he called them the Law of Calling and the Law of Crossing. GSB revived and clarified central aspects of Peirce's systems of logical graphs and I find it helpful to integrate his work into my exposition of Peirce. For now you can think of those as exemplifying two core formal principles which go to the root of the mathematical forms underlying logical reasoning.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Logical Graphs • Discussion 5<br />• <a href="https://inquiryintoinquiry.com/2023/08/28/logical-graphs-discussion-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/28/logical-graphs-discussion-5/</span></a></p><p>Re: Logical Graphs • First Impressions<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a><br />Re: Facebook • Daniel Everett <br />• <a href="https://www.facebook.com/permalink.php?story_fbid=pfbid026jD3t75k69Wbs9q3qaCAvTA6zb1GXCqwu4ZWfssxgGGd1er7Wwz8PyygiQUmF6t3l&id=100093271525294" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="ellipsis">facebook.com/permalink.php?sto</span><span class="invisible">ry_fbid=pfbid026jD3t75k69Wbs9q3qaCAvTA6zb1GXCqwu4ZWfssxgGGd1er7Wwz8PyygiQUmF6t3l&id=100093271525294</span></a></p><p>DE: Nice discussion. Development of icon-based reasoning.</p><p>My Comment —</p><p>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 …</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Logical Graphs • First Impressions 1<br />• <a href="https://inquiryintoinquiry.com/2023/08/24/logical-graphs-first-impressions/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/08</span><span class="invisible">/24/logical-graphs-first-impressions/</span></a></p><p>Introduction • Moving Pictures of Thought —</p><p>A “logical graph” is a graph-theoretic structure in one of the systems of graphical syntax Charles Sanders Peirce developed for logic.</p><p>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.</p><p>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.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a></p>
Jon Awbrey<p>Survey of Animated Logical Graphs<br />• <a href="https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/03</span><span class="invisible">/28/survey-of-animated-logical-graphs-5/</span></a></p><p>This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph-theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.</p><p>Please follow the above link for the full set of resources. A couple of beginning pieces are linked below.</p><p>Logical Graphs • Introduction<br />• <a href="https://inquiryintoinquiry.com/2008/07/29/logical-graphs-introduction/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2008/07</span><span class="invisible">/29/logical-graphs-introduction/</span></a></p><p>Logical Graphs • Formal Development<br />• <a href="https://inquiryintoinquiry.com/2008/09/19/logical-graphs-formal-development/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2008/09</span><span class="invisible">/19/logical-graphs-formal-development/</span></a></p><p>I've been thinking about ways to connect the species of logical graphs I've been developing out of Peirce's entitative and existential graphs with the styles of logical graphs envisioned in the RDF Surfaces group.</p><p>One thing arising out of those reflections was I began to tease apart two layers of structure, the one involved in conceiving and computing logical formulas and the other employed in displaying the end results.</p><p>At any rate, I'll explore that theme further as we go.</p><p>For now, the Survey page linked above will provide an overview of work already done.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <a href="https://mathstodon.xyz/tags/LogicAsSemiotics" class="mention hashtag" rel="tag">#<span>LogicAsSemiotics</span></a><br /><a href="https://mathstodon.xyz/tags/RelationTheory" class="mention hashtag" rel="tag">#<span>RelationTheory</span></a> <a href="https://mathstodon.xyz/tags/SignRelations" class="mention hashtag" rel="tag">#<span>SignRelations</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="tag">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/W3C" class="mention hashtag" rel="tag">#<span>W3C</span></a> <a href="https://mathstodon.xyz/tags/RDF" class="mention hashtag" rel="tag">#<span>RDF</span></a> <a href="https://mathstodon.xyz/tags/RDFSurfaces" class="mention hashtag" rel="tag">#<span>RDFSurfaces</span></a></p>
Jon Awbrey<p>Survey of Animated Logical Graphs<br />• <a href="https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2023/03</span><span class="invisible">/28/survey-of-animated-logical-graphs-5/</span></a></p><p>This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph-theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="tag">#<span>EntitativeGraphs</span></a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="tag">#<span>ExistentialGraphs</span></a><br /><a href="https://mathstodon.xyz/tags/Boole" class="mention hashtag" rel="tag">#<span>Boole</span></a> <a href="https://mathstodon.xyz/tags/BooleanAlgebra" class="mention hashtag" rel="tag">#<span>BooleanAlgebra</span></a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="tag">#<span>BooleanFunctions</span></a> <a href="https://mathstodon.xyz/tags/ModelTheory" class="mention hashtag" rel="tag">#<span>ModelTheory</span></a> <a href="https://mathstodon.xyz/tags/ProofTheory" class="mention hashtag" rel="tag">#<span>ProofTheory</span></a><br /><a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="tag">#<span>SpencerBrown</span></a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="tag">#<span>LawsOfForm</span></a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#<span>PropositionalCalculus</span></a> <a href="https://mathstodon.xyz/tags/LogicAsSemiotics" class="mention hashtag" rel="tag">#<span>LogicAsSemiotics</span></a></p>
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