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#logic

32 posts22 participants8 posts today
Public *
Inquiry Into Inquiry

Cactus Language • Discussion 1

Re: Cactus Language • Preliminaries 9
Re: Cybernetics • Joe Bury

JB: What does subcatenation and surcatenation mean?  Their definitions are not found in a dictionary.  I get the formulas you wrote but I don’t understand the meaning.

Thanks for the question, Joe,

The current presentation of Cactus Language is rather abstract and formal because that’s what we need for a fully computational parsing algorithm, and there’s quite a bit more to do on that score as we go, but I have written more intuitive introductions to the same material various times before — You might try one of the following for starters.

Keeping it short and simple as possible —

  • Under the Existential Interpretation
    • The syntactic connective of Concatenation is interpreted as the Logical Conjunction, which says all of its operands are true.
    • The syntactic connective of Surcatenation is interpreted as the Minimal Negation Operation, which says exactly one of its operands is false.
  • Under the Entitative Interpretation
    • The syntactic connective of Concatenation is interpreted as the Logical Disjunction, which says some of its operands are true.
    • The syntactic connective of Surcatenation is interpreted as the Dual of Minimal Negation, which says not just one of its operands is true.

Resources

cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Inquiry Into Inquiry · Cactus Language • Preliminaries 9
More from Inquiry Into Inquiry
#Automata#BooleanAlgebra#BooleanFunctions
Public
Philo Sophies

#Guest post by #Peter #Addor: “Is there anything beyond #space and #time?”

During his “travels through distant lands and #scientific #thoughts” he apparently came across the “terra incognita” of my #blog and here in particular the “sources of the origin of #logic”, which I tried to explore in my essay “Die #Metamathematik - ist doch #metalogisch?!?” (philosophies.de/index.php/2023), which I tried to explore.

More at: philosophies.de/index.php/2024

hands an geometrical figures
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Inquiry Into Inquiry

Survey of Theme One Program • 7

This is a Survey of resources 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, in particular, two‑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 implementation of an Automated Research Tool able to double as a platform for Inquiry Driven Education.

Wiki Hub

Documentation

Blog Series

Blog Dialogs

Applications

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, Toronto, Canada, pp. 874–875.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (January 1991), “Exploring Research Data Interactively • Developing a Computer Architecture for Inquiry”, Poster presented at the Annual Sigma Xi Research Forum, University of Texas Medical Branch, Galveston, TX.
  • 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, pp. 9–15.  Online.

cc: FB | Theme One Program • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Inquiry Into Inquiry · Surveys
More from Inquiry Into Inquiry
#Algorithms#Animata#ArtificialIntelligence
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Inquiry Into Inquiry

Survey of Semiotics, Semiosis, Sign Relations • 6

C.S. Peirce defines logic as “formal semiotic”, using formal to highlight the place of logic as a normative science, over and above the descriptive study of signs and their role in wider fields of play.  Understanding logic as Peirce understands it thus requires a companion study of semiotics, semiosis, and sign relations.

What follows is a Survey 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.

Elements

Sources

  • C.S. Peirce • Algebra of Logic ∫ Philosophy of Notation • (1) • (2)
  • C.S. Peirce • Algebra of Logic 1885 • Selections • (1) • (2) • (3) • (4)

Topics

Blog Series

  • Peircean Semiotics and Triadic Sign Relations • (1) • (2) • (3)

Blog Dialogs

Excursions

  • Semiositis • (1)
  • Signspiel • (1)
  • Skiourosemiosis • (1)

References

  • Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  Online.
  • Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.
  • Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), 40–52.  Archive.  Journal.  Online (doc) (pdf).
  • Awbrey, J.L., and Awbrey, S.M. (1992), “Interpretation as Action : The Risk of Inquiry”, The Eleventh International Human Science Research Conference, Oakland University, Rochester, Michigan.

cc: FB | Semeiotics • Laws of Form • Mathstodon • Ontolog • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

Inquiry Into Inquiry · Surveys
More from Inquiry Into Inquiry
#CSPeirce#IconIndexSymbol#Inquiry
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Ailrun (UTC-5/-4)

논리와 메모리 - 논리와 저수준(Low-level) 자료 표현(Data representation) (2 편 중 2 편)

hackers.pub/@ailrun/2025/%EB%8

Hackers' Pub · 논리와 메모리 - 논리와 저수준(Low-level) 자료 표현(Data representation) (2 편 중 2 편)이 글은 "논리적"이 되는 두 번째 방법인 논건 대수를 재조명하며, 특히 컴퓨터 공학적 해석에 초점을 맞춥니다. 기존 논건 대수의 한계를 극복하기 위해, 컷 규칙을 적극 활용하는 반(半)공리적 논건 대수(SAX)를 소개합니다. SAX는 추론 규칙의 절반을 공리로 대체하여, 메모리 주소와 접근자를 활용한 저수준 자료 표현과의 커리-하워드 대응을 가능하게 합니다. 글에서는 랜드(∧)와 로어(∨)를 "양의 방법", 임플리케이션(→)을 "음의 방법"으로 구분하고, 각 논리 연산에 대한 메모리 구조와 연산 방식을 상세히 설명합니다. 특히, init 규칙은 메모리 복사, cut 규칙은 메모리 할당과 초기화에 대응됨을 보여줍니다. 이러한 SAX의 컴퓨터 공학적 해석은 함수형 언어의 저수준 컴파일에 응용될 수 있으며, 논리와 컴퓨터 공학의 연결고리를 더욱 강화합니다. 프랭크 페닝 교수의 연구를 바탕으로 한 SAX는 현재도 활발히 연구 중인 체계로, ML 계열 언어 컴파일러 개발에도 기여할 수 있을 것으로 기대됩니다.
#data_representation#자료표현#semiaxiomatic_sequent_calculus
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