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Jon Awbrey<p>Cactus Language • Overview 3.2<br>• <a href="https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/07/cactus-language-overview-3/</span></a></p><p>Given a body of conceivable propositions we need a way to follow the threads of their indications from their object domain to their values for the mind and a way to follow those same threads back again. Moreover, we need to implement both ways of proceeding in computational form. Thus we need programs for tracing the clues sentences provide from the universe of their objects to the signs of their values and, in turn, from signs to objects. Ultimately, we need to render propositions so functional as indicators of sets and so essential for examining the equality of sets as to give a rule for the practical conceivability of sets. Tackling that task requires us to introduce a number of new definitions and a collection of additional notational devices, to which we now turn.</p><p>Resources —</p><p>Cactus Language • Overview<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Overview" rel="nofollow noopener" translate="no" target="_blank"><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>Survey of Animated Logical Graphs<br>• <a href="https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs-7/" rel="nofollow noopener" translate="no" target="_blank"><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 Theme One Program<br>• <a href="https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/" rel="nofollow noopener" translate="no" target="_blank"><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="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/AutomataTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AutomataTheory</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 3.1<br>• <a href="https://inquiryintoinquiry.com/2025/03/07/cactus-language-overview-3/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/07/cactus-language-overview-3/</span></a></p><p>In the development of Cactus Language to date the following two species of graphs have been instrumental.</p><p>• Painted And Rooted Cacti (PARCAI).<br>• Painted And Rooted Conifers (PARCOI).</p><p>It suffices to begin with the first class of data structures, developing their properties and uses in full, leaving discussion of the latter class to a part of the project where their distinctive features are key to developments at that stage. Partly because the two species are so closely related and partly for the sake of brevity, we'll always use the genus name “PARC” to denote the corresponding cacti.</p><p>To provide a computational middle ground between sentences seen as syntactic strings and propositions seen as indicator functions the language designer must not only supply a medium for the expression of propositions but also link the assertion of sentences to a means for inverting the indicator functions, that is, for computing the “fibers” or “inverse images” of the propositions.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/AutomataTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>AutomataTheory</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 2<br>• <a href="https://inquiryintoinquiry.com/2025/03/06/cactus-language-overview-2/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/06/cactus-language-overview-2/</span></a></p><p>In order to facilitate the use of propositions as indicator functions it helps to acquire a flexible notation for referring to propositions in that light, for interpreting sentences in a corresponding role, and for negotiating the requirements of mutual sense between the two domains. If none of the formalisms readily available or in common use meet all the design requirements coming to mind then it is necessary to contemplate the design of a new language especially tailored to the purpose.</p><p>In the present application, there is a pressing need to devise a general calculus for composing propositions, computing their values on particular arguments, and inverting their indications to arrive at the sets of things in the universe which are indicated by them. </p><p>For computational purposes it is convenient to have a middle ground or an intermediate language for negotiating between the “koine” of sentences regarded as strings of literal characters and the realm of propositions regarded as objects of logical value, even if that makes it necessary to introduce an artificial medium of exchange between the two domains.</p><p>If the necessary computations are to be carried out in an organized fashion, and ultimately or partially by familiar classes of machines, then the strings expressing logical propositions are likely to find themselves parsed into tree‑like data structures at some stage of the game. As far as their abstract structures as graphs are concerned, there are several species of graph‑theoretic data structures fitting the task in a reasonably effective and efficient way.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 1.2<br>• <a href="https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/01/cactus-language-overview-1/</span></a></p><p>Resource —</p><p>For readers interested and intrepid enough to read ahead, here’s an outline of my work in progress on the OEIS Wiki, which I’ll be revising and serializing to my Inquiry blog.</p><p>Part 1<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_1</span></a></p><p>Cactus Language • Syntax<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Syntax" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_1#Syntax</span></a></p><p>Part 2<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_2</span></a></p><p>Generalities About Formal Grammars<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_2#Generalities" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_2#Generalities</span></a></p><p>Part 3<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3</span></a></p><p>Cactus Language • Stylistics<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stylistics" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Stylistics</span></a></p><p>Cactus Language • Mechanics<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Mechanics" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Mechanics</span></a></p><p>Cactus Language • Semantics<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Semantics" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Semantics</span></a></p><p>Stretching Exercises<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_3#Stretching_Exercises" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Part_3#Stretching_Exercises</span></a></p><p>References<br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_References" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_References</span></a></p><p>Document History <br>• <a href="https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Document_History" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Cactus_Language_</span><span class="invisible">%E2%80%A2_Document_History</span></a></p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/Automata" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Automata</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Cactus Language • Overview 1.1<br>• <a href="https://inquiryintoinquiry.com/2025/03/01/cactus-language-overview-1/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2025/03</span><span class="invisible">/01/cactus-language-overview-1/</span></a></p><p>❝Thus, what looks to us like a sphere of scientific knowledge more accurately should be represented as the inside of a highly irregular and spiky object, like a pincushion or porcupine, with very sharp extensions in certain directions, and virtually no knowledge in immediately adjacent areas. If our intellectual gaze could shift slightly, it would alter each quill’s direction, and suddenly our entire reality would change.❞</p><p>— Herbert J. Bernstein • “Idols of Modern Science”</p><p>The following report describes a calculus for representing propositions as sentences, that is, as syntactically defined sequences of signs, and for working with those sentences in light of their semantically defined contents as logical propositions. In their computational representation the expressions of the calculus parse into a class of graph‑theoretic data structures whose underlying graphs are called “painted cacti”.</p><p>Painted cacti are a specialization of what graph‑theorists refer to as “cacti”, which are in turn a generalization of what they call “trees”. The data structures corresponding to painted cacti have especially nice properties, not only useful in computational terms but interesting from a theoretical standpoint. The remainder of the present Overview is devoted to motivating the development of the indicated family of formal languages, going under the generic name of Cactus Language.</p><p><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/Semiotics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Semiotics</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DifferentialLogic</span></a> <br><a href="https://mathstodon.xyz/tags/Automata" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Automata</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a> <a href="https://mathstodon.xyz/tags/FormalGrammars" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalGrammars</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a></p>
Jon Awbrey<p>Theme One Program • Motivation 1<br>• <a href="https://inquiryintoinquiry.com/2024/06/03/theme-one-program-motivation-1-b/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/06</span><span class="invisible">/03/theme-one-program-motivation-1-b/</span></a></p><p>The main idea behind the Theme One program is the efficient use of graph‑theoretic data structures for the tasks of “learning” and “reasoning”.</p><p>I am thinking of “learning” in the sense of learning about an environment, in essence, gaining information about the nature of an environment and being able to apply the information acquired to a specific purpose.</p><p>Under the heading of “reasoning” I am simply lumping together all the ordinary sorts of practical activities which would probably occur to most people under that name.</p><p>There is a natural relation between the tasks. Learning the character of an environment leads to the recognition of laws which govern the environment and making full use of that recognition requires the ability to reason logically about those laws in abstract terms.</p><p>Resources —</p><p>Theme One Program • Overview<br>• <a href="https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Theme_One_Progra</span><span class="invisible">m_%E2%80%A2_Overview</span></a></p><p>Theme One Program • Exposition<br>• <a href="https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Theme_One_Progra</span><span class="invisible">m_%E2%80%A2_Exposition</span></a></p><p>Theme One Program • User Guide<br>• <a href="https://www.academia.edu/5211369/Theme_One_Program_User_Guide" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">academia.edu/5211369/Theme_One</span><span class="invisible">_Program_User_Guide</span></a></p><p>Survey of Theme One Program<br>• <a href="https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/" rel="nofollow noopener" translate="no" target="_blank"><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/ThemeOneProgram" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ThemeOneProgram</span></a> <a href="https://mathstodon.xyz/tags/Learning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Learning</span></a> <a href="https://mathstodon.xyz/tags/Reasoning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Reasoning</span></a> <br><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a> <br><a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a> <a href="https://mathstodon.xyz/tags/DataStructure" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DataStructure</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a> <br><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/PragmaticSemioticInformation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PragmaticSemioticInformation</span></a> <br><a href="https://mathstodon.xyz/tags/Empiricism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Empiricism</span></a> <a href="https://mathstodon.xyz/tags/Rationalism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Rationalism</span></a> <a href="https://mathstodon.xyz/tags/Pragmatism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Pragmatism</span></a></p>
marco<p>Today (3PM GMT, May 15), I will be hosting this week&#39;s Formal Language and Neural Networks (FLaNN - <a href="https://flann.super.site/" target="_blank" rel="nofollow noopener" translate="no"><span class="invisible">https://</span><span class="">flann.super.site/</span><span class="invisible"></span></a>) seminar. </p><p>The speaker is Frank Drewes from Umeå University, who will be talking about Graph Extension Grammars.</p><p>This is a fantastic weekly seminar focusing on the interpretability and computational power of neural language models, especially as related to formal languages.</p><p>Check out the site for past and future talks! </p><p><a href="https://sigmoid.social/tags/ML" class="mention hashtag" rel="tag">#<span>ML</span></a> <a href="https://sigmoid.social/tags/Interpretability" class="mention hashtag" rel="tag">#<span>Interpretability</span></a> <a href="https://sigmoid.social/tags/FormalLanguages" class="mention hashtag" rel="tag">#<span>FormalLanguages</span></a></p>
Jon Awbrey<p>Theme One Program • Exposition 1.2<br>• <a href="https://inquiryintoinquiry.com/2022/06/15/theme-one-program-exposition-1-2/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2022/06</span><span class="invisible">/15/theme-one-program-exposition-1-2/</span></a></p><p>The Idea↑Form Flag</p><p>The graph-theoretic data structures used by the program are built up from a basic data structure called an “idea-form flag”. That structure is defined as a pair of Pascal data types by means of the following specifications.</p><p>Figure 1. Type Idea = ^Form<br>• <a href="https://inquiryintoinquiry.files.wordpress.com/2022/06/theme-exposition-type-idea-5eform.png" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.files.wordp</span><span class="invisible">ress.com/2022/06/theme-exposition-type-idea-5eform.png</span></a></p><p>Figure 2. Code Box<br>• type idea = ^form;<br>• form = record<br>• sign: char;<br>• as, up, on, by: idea;<br>• code: numb<br>• end;</p><p>An “idea” is a pointer to a “form”.<br>• A “form” is a record consisting of:<br>• A “sign” of type “char”;<br> • Four pointers, “as”, “up”, “on”, “by”, of type “idea”;<br> • A “code” of type “numb”, that is, an integer in [0, max integer].</p><p>Represented in terms of “digraphs”, or directed graphs, the combination of an idea pointer and a form record is most easily pictured as an “arc”, or directed edge, leading to a node labeled with the other data, in this case, a letter and a number.</p><p><a href="https://mathstodon.xyz/tags/ThemeOneProgram" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ThemeOneProgram</span></a> <a href="https://mathstodon.xyz/tags/Learning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Learning</span></a> <a href="https://mathstodon.xyz/tags/Reasoning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Reasoning</span></a><br><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a><br><a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a> <a href="https://mathstodon.xyz/tags/DataStructure" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DataStructure</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a><br><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/PragmaticSemioticInformation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PragmaticSemioticInformation</span></a><br><a href="https://mathstodon.xyz/tags/Empiricism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Empiricism</span></a> <a href="https://mathstodon.xyz/tags/Rationalism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Rationalism</span></a> <a href="https://mathstodon.xyz/tags/Pragmatism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Pragmatism</span></a></p>
Jon Awbrey<p>Theme One Program • Exposition 1.1<br>• <a href="https://inquiryintoinquiry.com/2024/06/09/theme-one-program-exposition-1-b/" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">inquiryintoinquiry.com/2024/06</span><span class="invisible">/09/theme-one-program-exposition-1-b/</span></a></p><p>Theme One is a program for constructing and transforming a particular species of graph‑theoretic data structures, forms designed to support a variety of fundamental learning and reasoning tasks.</p><p>The program evolved over the course of an exploration into the integration of contrasting types of activities involved in learning and reasoning, especially the types of algorithms and data structures capable of supporting all sorts of inquiry processes, from everyday problem solving to scientific investigation. In its current state, Theme One integrates over a common data structure fundamental algorithms for one type of inductive learning and one type of deductive reasoning.</p><p>We begin by describing the class of graph-theoretic data structures used by the program, as determined by their local and global features. It will be the usual practice to shift around and view these graphs at many different levels of detail, from their abstract definition to their concrete implementation, and many points in between.</p><p>The main work of the Theme One program is achieved by building and transforming a single species of graph-theoretic data structures. In their abstract form these structures are closely related to the graphs called cacti and conifers in graph theory, so we’ll generally refer to them under those names.</p><p><a href="https://mathstodon.xyz/tags/ThemeOneProgram" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ThemeOneProgram</span></a> <a href="https://mathstodon.xyz/tags/Learning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Learning</span></a> <a href="https://mathstodon.xyz/tags/Reasoning" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Reasoning</span></a><br><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Logic</span></a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>LogicalGraphs</span></a> <a href="https://mathstodon.xyz/tags/FormalLanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FormalLanguages</span></a><br><a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a> <a href="https://mathstodon.xyz/tags/DataStructure" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>DataStructure</span></a> <a href="https://mathstodon.xyz/tags/GraphTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GraphTheory</span></a><br><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Peirce</span></a> <a href="https://mathstodon.xyz/tags/PragmaticSemioticInformation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PragmaticSemioticInformation</span></a><br><a href="https://mathstodon.xyz/tags/Empiricism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Empiricism</span></a> <a href="https://mathstodon.xyz/tags/Rationalism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Rationalism</span></a> <a href="https://mathstodon.xyz/tags/Pragmatism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Pragmatism</span></a></p>
marco<p>There are a four invited speakers, but I am only personally familiar with three (Cyril Allauzen @ Google, Will Merrill @ NYU/Google, and Dana Angluin @ Yale).</p><p>These three talks should be fantastic, especially if you are interested in <a href="https://sigmoid.social/tags/automata" class="mention hashtag" rel="tag">#<span>automata</span></a>, <a href="https://sigmoid.social/tags/FormalLanguages" class="mention hashtag" rel="tag">#<span>FormalLanguages</span></a>, and <a href="https://sigmoid.social/tags/Interpretability" class="mention hashtag" rel="tag">#<span>Interpretability</span></a> in neural language models!</p><p>(Plugging <a href="https://flann.super.site/" target="_blank" rel="nofollow noopener" translate="no"><span class="invisible">https://</span><span class="">flann.super.site/</span><span class="invisible"></span></a> if those sound cool to you)</p>
Marco 🌳 Zocca<p>three days for nailing the correct order of parser combinators for a large language 🫠</p><p>I think I&#39;ll need to add Bison/Yacc to my toolbelt</p><p><a href="https://sigmoid.social/tags/proglang" class="mention hashtag" rel="tag">#<span>proglang</span></a> <a href="https://sigmoid.social/tags/plt" class="mention hashtag" rel="tag">#<span>plt</span></a> <a href="https://sigmoid.social/tags/formallanguages" class="mention hashtag" rel="tag">#<span>formallanguages</span></a> <a href="https://sigmoid.social/tags/compilers" class="mention hashtag" rel="tag">#<span>compilers</span></a></p>
EscalatedQuickly :hecked:<p>Might as well toot an <a href="https://infosec.exchange/tags/introduction" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>introduction</span></a> as well.</p><p>I've been here since 2019 according to my profile, but haven't tooted once until today.</p><p>I'm a <a href="https://infosec.exchange/tags/cybersecurity" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>cybersecurity</span></a> consultant who mainly does offensive security, but I very much enjoy picking apart <a href="https://infosec.exchange/tags/malware" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>malware</span></a> given the opportunity. I'm also technically a Ph.D. student researching metamorphic malware packers, but right now I'm on a hiatus from academia.</p><p>Other than <a href="https://infosec.exchange/tags/security" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>security</span></a> I'm also drawn to completely normal things, like <a href="https://infosec.exchange/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>categorytheory</span></a>, <a href="https://infosec.exchange/tags/formallanguages" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>formallanguages</span></a>, <a href="https://infosec.exchange/tags/osdev" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>osdev</span></a>, and most recently the <a href="https://infosec.exchange/tags/mainframe" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mainframe</span></a>. I'm also passionate about <a href="https://infosec.exchange/tags/foss" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>foss</span></a>, <a href="https://infosec.exchange/tags/unix" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>unix</span></a>, <a href="https://infosec.exchange/tags/linux" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>linux</span></a>, <a href="https://infosec.exchange/tags/openaccess" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>openaccess</span></a> and stuff like that.</p>