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by Jon Awbrey

Cf: Survey of Inquiry Driven Systems • 5 https://inquiryintoinquiry.com/2023/04/23/survey-of-inquiry-driven-systems-… All, This is a Survey of work in progress on Inquiry Driven Systems, material I plan to refine toward a more compact and systematic treatment of the subject. An “inquiry driven system” is a system having among its state variables some representing its state of information with respect to various topics of interest, for example, its own state and the states of any potential object systems. Thus it has a component of state tracing a trajectory though an “information state space”. Please follow the above link for the full set of resources. Articles treating the more central ideas are linked below. Elements — Prospects for Inquiry Driven Systems • https://oeis.org/wiki/User:Jon_Awbrey/Prospects_for_Inquiry_Driven_Systems Introduction to Inquiry Driven Systems • https://oeis.org/wiki/Introduction_to_Inquiry_Driven_Systems Background — Functional Logic • Inquiry and Analogy • https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy Functional Logic • Quantification Theory • https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Quantification_Theory Functional Logic • Higher Order Propositions • https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Higher_Order_Propositions Developments — Inquiry Driven Systems • Inquiry Fields • https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Inquiry_Fields Inquiry Driven Systems • Inquiry Into Inquiry • https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview Applications — Interpretation as Action • The Risk of Inquiry • https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inqui… An Architecture for Inquiry • Building Computer Platforms for Discovery • https://www.academia.edu/1270327/An_Architecture_for_Inquiry_Building_Compu… Exploring Research Data Interactively • Theme One : A Program of Inquiry • https://www.academia.edu/1272839/Exploring_Research_Data_Interactively._The… Conceptual Barriers to Creating Integrative Universities • https://org.sagepub.com/content/8/2/269.abstract Regards, Jon

1 year, 6 months

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Relation Theory

by Jon Awbrey

Cf: Survey of Relation Theory • 6 https://inquiryintoinquiry.com/2023/04/01/survey-of-relation-theory-6/ All, In this Survey of blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of which arise quite naturally in applications. This approach to relation theory is distinct from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other. Please follow the above link for the full set of resources. A few basic articles are linked below. Elements — • Relation Theory ( https://oeis.org/wiki/Relation_theory ) Relational Concepts — • Relation Construction ( https://oeis.org/wiki/Relation_construction ) • Relation Composition ( https://oeis.org/wiki/Relation_composition ) • Relation Reduction ( https://oeis.org/wiki/Relation_reduction ) • Relative Term ( https://oeis.org/wiki/Relative_term ) • Sign Relation ( https://oeis.org/wiki/Sign_relation ) • Triadic Relation ( https://oeis.org/wiki/Triadic_relation ) • Logic of Relatives ( https://oeis.org/wiki/Logic_of_relatives ) • Hypostatic Abstraction ( https://oeis.org/wiki/Hypostatic_abstraction ) • Continuous Predicate ( https://oeis.org/wiki/Continuous_predicate ) Illustrations — Six Ways of Looking at a Triadic Relation ⌬ 1 • https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-… Peirce's 1870 “Logic of Relatives” — Overview • https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-o… Preliminaries • https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-p… Regards, Jon

1 year, 6 months

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Theme One Program • Discussion

by Jon Awbrey

Cf: Theme One Program • Discussion 10 https://inquiryintoinquiry.com/2023/04/17/theme-one-program-discussion-10/ Re: Mathstodon • Seamus Bradley ::: https://mathstodon.xyz/@Scmbradley/110198310724722597 <QUOTE SB:> I thought of a programming language where every function can only return one type: the return type. The return type is just a wrapper around a struct that contains the actual return value, but also a reference to the called function and arguments, and possibly an error code. </QUOTE> My flashback — Way back in the last millennium I started work on a programming style I called an “idea processor”, where an “idea” is a pointer to a “form” and a form is a minimal type of record containing 1 character, 1 number, and 4 more ideas. I implemented a functional style where all the main functions are transformations of one or more ideas to a return idea. The principal data type is an “idea-form flag” which serves a role analogous to a “cons cell” in Lisp. Here's one entry point — Theme One Program • Exposition 1 • https://inquiryintoinquiry.com/2022/06/15/theme-one-program-exposition-1-2/ Regards, Jon ( https://mathstodon.xyz/@Inquiry )

1 year, 7 months

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Semiotics, Semiosis, Sign Relations

by Jon Awbrey

Cf: Survey of Semiotics, Semiosis, Sign Relations • 4 https://inquiryintoinquiry.com/2023/04/05/survey-of-semiotics-semiosis-sign… All, C.S. Peirce defines “logic” as “formal semiotic”, using “formal” to distinguish the role of logic as a normative science, over and above the more descriptive study of signs in the wild and their antics at large. Understanding logic as Peirce understood it therefore requires a companion study of semiotics, semiosis, and sign relations. This is a Survey ( https://inquiryintoinquiry.com/surveys/ ) of blog and wiki resources on the theory of signs, variously known as semeiotic or semiotics, and the actions referred to as semiosis which transform signs among themselves in relation to their objects, all as based on C.S. Peirce's concept of triadic sign relations. Note. Please follow the above link for the full set of resources. I'll post just a sample of basics below. Elements • Semeiotic ( https://oeis.org/wiki/Semeiotic ) • Sign Relations ( https://oeis.org/wiki/Sign_relation ) Sources C.S. Peirce • On the Definition of Logic https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-on-the-definition-of-l… C.S. Peirce • Logic as Semiotic https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-logic-as-semiotic/ C.S. Peirce • Objective Logic https://inquiryintoinquiry.com/2012/03/09/c-s-peirce-objective-logic/ Blog Series • Semeiotic ( https://inquiryintoinquiry.com/2008/07/30/semeiotic/ ) Regards, Jon ( https://mathstodon.xyz/@Inquiry )

1 year, 7 months

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Definition and Determination

by Jon Awbrey

Cf: Survey of Definition and Determination • 2 https://inquiryintoinquiry.com/2023/04/06/survey-of-definition-and-determin… All, In the early 1990s, “in the middle of life's journey” as the saying goes, I returned to grad school in a systems engineering program with the idea of taking a more systems-theoretic approach to my development of Peircean themes, from signs and scientific inquiry to logic and information theory. Two of the first questions calling for fresh examination were the closely related concepts of definition and determination, not only as Peirce used them in his logic and semiotics but as researchers in areas as diverse as computer science, cybernetics, physics, and systems sciences were finding themselves forced to reconsider the concepts in later years. That led me to collect a sample of texts where Peirce and a few other writers discuss the issues of definition and determination. There are copies of those selections at the following sites. Collection Of Source Materials • https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS Excerpts on Definition • https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Definition Excerpts on Determination • https://oeis.org/wiki/User:Jon_Awbrey/EXCERPTS#Determination What follows is a Survey of blog and wiki posts on Definition and Determination, with a focus on the part they play in Peirce's interlinked theories of signs, information, and inquiry. In classical logical traditions the concepts of definition and determination are closely related and their bond acquires all the more force when we view the overarching concept of constraint from an information-theoretic point of view, as Peirce did beginning in the 1860s. Regards, Jon https://mathstodon.xyz/@Inquiry

1 year, 7 months

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Animated Logical Graphs

by Jon Awbrey

All, 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. 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. At any rate, I'll be exploring that theme further as we go ... For now, here's one overview of some work already done — Cf: Survey of Animated Logical Graphs https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs… 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. Please follow the link above for the full set of resources. For now I'll just give links to a couple of beginning pieces. Logical Graphs • Introduction https://inquiryintoinquiry.com/2008/07/29/logical-graphs-introduction/ Logical Graphs • Formal Development https://inquiryintoinquiry.com/2008/09/19/logical-graphs-formal-development/ Regards, Jon https://inquiryintoinquiry.com/ https://mathstodon.xyz/@Inquiry

1 year, 7 months

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Theme One Program

by Jon Awbrey

Cf: Survey of Theme One Program • 5 https://inquiryintoinquiry.com/2023/03/30/survey-of-theme-one-program-5/ All, Updating my Survey post on the Theme One Program for the use of the W3 RDF Surfaces working group. ⁂ This is a Survey ( https://inquiryintoinquiry.com/surveys/ ) of blog and wiki posts relating to the Theme One Program I worked on all through the 1980s. The aim was to develop fundamental algorithms and data structures for integrating empirical learning with logical reasoning. I had earlier developed separate programs for basic components of those tasks, namely, 2-level formal language learning and propositional constraint satisfaction, the latter using an extension of C.S. Peirce's logical graphs as a syntax for propositional logic. Thus arose the question of how well it might be possible to get “empiricist” and “rationalist” modes of operation to cooperate. The long-term vision is the design and implementation of an Automated Research Tool able to double as a platform for Inquiry Driven Education. Note. Please follow the above link for the full set of resources. I'll post just a sample of basics below. Wiki Hub ======== • Theme One Program • Overview ( https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview ) Documentation ============= • Theme One Program • Pascal Source Code ( https://www.academia.edu/5210987/Theme_One_Program_Pascal_Source_Code ) • Theme One Program • User Guide ( https://www.academia.edu/5211369/Theme_One_Program_User_Guide ) • Theme One Program • Exposition ( https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition ) Applications ============ Applications, Examples, Exercises • Jets and Sharks ( https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks… ) ( https://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks… ) ( https://inquiryintoinquiry.com/2022/09/03/theme-one-program-jets-and-sharks… ) • Applications of a Propositional Calculator • Constraint Satisfaction Problems ( https://www.academia.edu/4727842/Applications_of_a_Propositional_Calculator… ) • Exploratory Qualitative Analysis of Sequential Observation Data ( https://oeis.org/wiki/User:Jon_Awbrey/Exploratory_Qualitative_Analysis_of_S… ) References ========== Awbrey, S.M., and Awbrey, J.L. (May 1991), “An Architecture for Inquiry : • Building Computer Platforms for Discovery”, Proceedings of the Eighth International Conference on Technology and Education. ( https://www.academia.edu/1270327/An_Architecture_for_Inquiry_Building_Compu… ) Awbrey, J.L., and Awbrey, S.M. (August 1990), “Exploring Research Data Interactively • Theme One : A Program of Inquiry”, Proceedings of the Sixth Annual Conference on Applications of Artificial Intelligence and CD-ROM in Education and Training, Society for Applied Learning Technology, Washington, DC. ( https://www.academia.edu/1272839/Exploring_Research_Data_Interactively._The… ) Regards, Jon https://mathstodon.xyz/@Inquiry

1 year, 7 months

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Differential Logic and Dynamic Systems

by Jon Awbrey

Cf: Differential Logic and Dynamic Systems • Overview https://inquiryintoinquiry.com/2019/09/10/differential-logic-and-dynamic-sy… All, In modeling intelligent systems, whether we are trying to understand a natural system or engineer an artificial system, there has long been a tension or trade-off between dynamic paradigms and symbolic paradigms. Dynamic models take their cue from physics, using quantitative measures and differential equations to model the evolution of a system’s state through time. Symbolic models use logical methods to describe systems and their agents in qualitative terms, deriving logical consequences of a system’s description or an agent’s state of information. Logic-based systems have tended to be static in character, largely because we have lacked a proper logical analogue of differential calculus. The work laid out in this series of posts is intended to address that lack. Note: The links below will take you to the current OEIS Wiki version of a project I began under the auspices of a Systems Engineering program at Oakland University. I'm about to be shanghaied into a mess of long put off chores but some time this summer I hope to get back to revising the text, redoing the graphics messed over by long ago Mac to PC platform changes, and serializing the content to my blog. Overview : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Over… Part 1 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Part 2 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Part 3 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Part 4 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Part 5 : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Part… Appendices : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Appe… References : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Refe… Doc History : https://oeis.org/wiki/Differential_Logic_and_Dynamic_Systems_%E2%80%A2_Docu… Regards, Jon

1 year, 8 months

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In the Way of Inquiry

by Jon Awbrey

Cf: In the Way of Inquiry • Recircus http://inquiryintoinquiry.com/2023/01/06/in-the-way-of-inquiry-recircus-2/ “I must lie down where all the ladders start In the foul rag and bone shop of the heart.” — W.B. Yeats https://web.archive.org/web/20200402124816/https://www.web-books.com/Classi… All, I was never on Twitter but many people whose writings I follow here and there on the web often reshared their posts from there. So when a horde of them began migrating to Fediverse locales like Mastodon and especially Mathstodon (where they have LaTeX) I took a chance on tagging along. I don't know whether micro-blooging is really my medium yet but the diversity of readings from others has been pretty interesting so far. It's also serving as a beneficial exercise trying to quantize my macro-bloggings down to micro scale, so I'll keep working at that for the time being and see how it goes. For now I have in mind circling back to a point in my project on Inquiry Driven Systems, namely, the chapter addressing various Obstacles to the Project. Inquiry Driven Systems • Overview https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Overview Inquiry Driven Systems • Obstacles https://oeis.org/wiki/Inquiry_Driven_Systems_%E2%80%A2_Part_5#Obstacles Regards, Jon (https://mathstodon.xyz/@Inquiry)

1 year, 8 months

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Riffs and Rotes

by Jon Awbrey

Cf: Riffs and Rotes • Happy New Year 2023 !!! https://inquiryintoinquiry.com/2023/01/01/riffs-and-rotes-happy-new-year-20… All, Let pₙ = the n-th prime. Then 2023 = 7∙17² = p₄∙p₇² = p_{p₁^p₁} ∙ {p_{p₄}}^{p₁} = p_{p₁^p₁} ∙ {p_{p_{p₁^p₁}}}^{p₁} No information is lost by dropping the terminal 1s. Thus we may write the following form. 2023 = p_{p^p} ∙ {p_{p_{p^p}}}^p Forms like those correspond to a family of digraphs called “riffs” and a family of graphs called “rotes”, as described in the following OEIS Wiki article. Riffs and Rotes ( https://oeis.org/wiki/Riffs_and_Rotes ) The riff and rote for 2023 are shown in the next two Figures. Riff 2023 https://inquiryintoinquiry.files.wordpress.com/2023/01/riff-2023-big-1.jpg Rote 2023 https://inquiryintoinquiry.files.wordpress.com/2023/01/rote-2023-big-1.jpg Regards, Jon ( https://mathstodon.xyz/@Inquiry )

1 year, 10 months

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CG