Language Learning And Logical Modeling —

Wrote my first “Language Learning Module”, strictly speaking, a two‑level formal language learner, back in the 80s and it pretty much told me what every conceivable upscale of that ilk would be like. But it did not cross the threshold of logical reasoning, so I used Peirce's logical graphs for that. Et sic deinceps …

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs
#LanguageLearningAlgorithm #LogicalModelingAlgorithm

Show HN: Meaning forks. SRT sees it
SRT(Semiotic-Reflexive Transformer)는 기존의 동결된 인과 언어 모델에 경량의 반사적 의미 인식 모듈을 추가하는 어댑터 아키텍처이다. 이 모듈들은 의미의 분기점을 감지하고, 모델이 자신의 의미 처리 과정을 반성적으로 인지하며, 필요시 의미적 수정을 주입한다. 7B 규모의 백본 모델은 완전히 고정되고, 약 1,460만 개의 파라미터만 학습되어 빠른 훈련이 가능하며, 다양한 백본 모델에 적용할 수 있다. SRT는 C.S. 퍼스의 기호학 이론에 기반하여, 단어가 서로 다른 커뮤니티에서 다르게 해석되는 현상을 모델이 인지하도록 설계되었다.

https://github.com/space-bacon/SRT

#transformer #adapter #languagemodel #semiotics #nlp

Animated Logical Graphs • 2
• https://inquiryintoinquiry.com/2015/01/14/animated-logical-graphs-2/

It's almost 50 years now since I first encountered the volumes of Peirce's “Collected Papers” in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown's “Laws of Form” in the Whole Earth Catalog and I sent off for it right away. I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph‑theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.

I thought it might contribute to a number of long‑running and ongoing discussions if I could articulate what I think I learned from that experience.

So I'll try to keep focused on that.

Resources —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

Animated Logical Graphs • 1
• https://inquiryintoinquiry.com/2015/01/08/animated-logical-graphs-1/

For Your Musement …

Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce's Alpha Graphs for propositional logic.

Proof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations

Double Negation
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-double-negation-2.0.gif

Peirce's Law
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-peirces-law-2.0.gif

Praeclarum Theorema
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-praeclarum-theorema-2.0.gif

Two‑Thirds Majority Function
• https://inquiryintoinquiry.com/wp-content/uploads/2026/04/proof-animation-e280a2-two-thirds-majority-function-2.0.gif

A full discussion of logical graphs can be found in the following article.

Logical Graphs
• https://oeis.org/wiki/Logical_Graphs

Resources —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2025/05/02/survey-of-animated-logical-graphs-8/

cc: https://www.academia.edu/community/ldzadj
cc: https://mathstodon.xyz/@Inquiry/116494097283214718
cc: https://www.researchgate.net/post/Animated_Logical_Graphs
cc: https://stream.syscoi.com/2026/04/30/animated-logical-graphs-1/
cc: https://groups.io/g/lawsofform/topic/animated_logical_graphs/119049814

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

Animated Logical Graphs • 1
• https://inquiryintoinquiry.com/2015/01/08/animated-logical-graphs-1/

For Your Musement …

Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

Proof Animations
• https://oeis.org/wiki/User:Jon_Awbrey/ANIMATION#Proof_Animations

See the following article for a full discussion of this type of logical graph.

Logical Graphs
• https://oeis.org/wiki/Logical_Graphs

Additional Resources —

Logical Graphs • First Impressions
• https://inquiryintoinquiry.com/2024/08/26/logical-graphs-first-impressions-a/

Logical Graphs • Formal Development
• https://inquiryintoinquiry.com/2024/09/12/logical-graphs-formal-development-b/

#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs #GraphTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #ProofAnimations

Just a thought: Sense is not given, but arises in conscious experience and is constantly reconstructed through language and relationships... We don't find sense in the lost property office. – Well, it's just a thought ;-)

#poetry
#semiotics

sense is no lost item
no quiet stone
in the dust of the world—
it grows in the gaze
that lingers

between breath and meaning
fine threads—
silent
until they speak

we are the language of our hours
the answer
shaped in time—

each nearness
writes us anew

Reflection On Recursion • Discussion 1
• https://inquiryintoinquiry.com/2026/04/21/reflection-on-recursion-discussion-1/

Re: Reflection On Recursion • 1
• https://inquiryintoinquiry.com/2026/04/06/reflection-on-recursion-1/
Re: Laws of Form • John Mingers
• https://groups.io/g/lawsofform/message/4943

JM:
❝This is a very important and interesting topic. I think you should consider the relationship to self‑reference, indeed are they really the same thing?

❝Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.❞

Thanks, John. Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few. But one thing I need to emphasize from the start is how radically different such concepts appear when viewed in the x‑ray vision of Peirce’s pragmatic semiotics.

I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

After a while, it simply becomes time to change the paradigm …

Just by way of a first example, take the very idea of “self‑reference”. The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.

And when we ask, “What is this, that we call an interpreter?”, the pragmatic theory of signs tells us we cannot tell when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

Et sic deinceps …

#Peirce #Logic #Mathematics
#Recursion #Reflection #Semiotics
#SignRelations #TriadicRelations

Reflection On Recursion • Discussion 1

Re: Reflection On Recursion • 1
Re: Laws of Form • John Mingers

Also the work of Maturana and Varela on autopoiesis and the neurophysiology of cognition which also has recursion at its heart.

Thanks, John.  Yes, we certainly find the whole array of self concepts coming into play here — selfhood, autopoiesis or self creation, self reference and self transformation, just to name a few.  But one thing I need to emphasize from the start is how radically different such concepts appear when viewed under x‑rays of Peirce’s pragmatic semiotics.

I forget where I first heard it, but it’s fairly common observation that the persistence of a recurring problem is a symptom of how unlikely it is to be solved in the paradigm where it keeps occurring.

After a while, it simply becomes time to change the paradigm …

Just by way of a first example, take the very idea of “self‑reference”.  The moment we place it in the medium of triadic sign relations we realize signs do not refer to anything at all except insofar as an interpreter refers them.  And when we think to ask, “What is this that we call an interpreter?”, the pragmatic theory of signs tells us we do not know when we turn out the light but under the x‑ray of the pragmatic maxim the sum of its effects is effectively modeled by an extended triadic sign relation.

Everything I’ll be working at here will be done within a framework like that.

Regards,
Jon

Resources

• Inquiry Driven Systems • Inquiry Into Inquiry
• Reflective Interpretive Frameworks
• The Phenomenology of Reflection
• Higher Order Sign Relations

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