Loet, All ...
Many thanks for the link to your paper! Just off-hand this looks like
the right ballpark for my long run interests but it will take me a few
more posts just dusting off home plate and chalking in some base lines.
Here's a paper Susan Awbrey and I wrote a while back giving some hint
of the Big Game in play here, the “scholarship of integration” needed
to bring the harvests of information locked away in so many isolated
silos to bear on our world of common problems.
https://www.academia.edu/1266492/Conceptual_Barriers_to_Creating_Integrative_Universities
Regards,
Jon
On 5/23/2020 9:18 AM, Loet Leydesdorff wrote:
Dear Jon,
I extensively use triads in a new paper:
Leydesdorff, Loet and Ivanova, Inga, The Measurement of 'Interdisciplinarity' and 'Synergy' in Scientific and
Extra-Scientific Collaborations (May 17, 2020). Available at SSRN: https://ssrn.com/abstract=3560339 or
http://dx.doi.org/10.2139/ssrn.3560339 <https://dx.doi.org/10.2139/ssrn.3560339>
You may find it interesting.
Best,
Loet
--------------------------------------------------------------------------------
Loet Leydesdorff
Professor emeritus, University of Amsterdam
Amsterdam School of Communication Research (ASCoR)
[email protected] <mailto:[email protected]>; http://www.leydesdorff.net/
Associate Faculty, SPRU, <http://www.sussex.ac.uk/spru/>University of Sussex;
Guest Professor Zhejiang Univ. <http://www.zju.edu.cn/english/>, Hangzhou; Visiting Professor, ISTIC,
<http://www.istic.ac.cn/Eng/brief_en.html>Beijing;
Visiting Fellow, Birkbeck <http://www.bbk.ac.uk/>, University of London;
http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en
ORCID: http://orcid.org/0000-0002-7835-3098;
------ Original Message ------
From: "Jon Awbrey" <[email protected]>
To: "Cybernetic Communications" <[email protected]>; "Ontolog Forum" <[email protected]>; "Peirce
List" <[email protected]>; "Structural Modeling" <[email protected]>; "SysSciWG"
<[email protected]>
Sent: 5/22/2020 3:45:08 PM
Subject: [CYBCOM] Re: Triadic Relations
Cf: Triadic Relations • 1
At: http://inquiryintoinquiry.com/2020/05/21/triadic-relations-%e2%80%a2-1/
Examples from Mathematics
=========================
For the sake of topics to be taken up later, it is useful to examine
a pair of triadic relations in tandem. We will construct two triadic
relations, L₀ and L₁, each of which is a subset of the same cartesian
product X × Y × Z. The structures of L₀ and L₁ can be described in
the following way.
Each space X, Y, Z is isomorphic to the boolean domain B = {0, 1}
so L₀ and L₁ are subsets of the cartesian power B × B × B or the
boolean cube B³.
The operation of boolean addition, + : B × B → B, is equivalent to
addition modulo 2, where 0 acts in the usual manner but 1 + 1 = 0.
In its logical interpretation, the plus sign can be used to indicate
either the boolean operation of exclusive disjunction or the boolean
relation of logical inequality.
The relation L₀ is defined by the following formula.
L₀ = { (x, y, z) ∈ B³ : x + y + z = 0 }.
The relation L₀ is the following set of four triples in B³.
L₀ = { (0, 0, 0), (0, 1, 1), (1, 0, 1), (1, 1, 0) }.
The relation L₁ is defined by the following formula.
L₁ = { (x, y, z) ∈ B³ : x + y + z = 1 }.
The relation L₁ is the following set of four triples in B³.
L₁ = { (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 1, 1) }.
The triples in the relations L₀ and L₁ are conveniently arranged
in the form of relational data tables, as shown below.
Triadic Relation L₀
https://inquiryintoinquiry.files.wordpress.com/2020/05/triadic-relation-l0-bit-sum-0.png
Triadic Relation L₁
https://inquiryintoinquiry.files.wordpress.com/2020/05/triadic-relation-l1-bit-sum-1.png
Resources
=========
• Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
• Sign Relations ( https://oeis.org/wiki/Sign_relation )
• Triadic Relations ( https://oeis.org/wiki/Triadic_relation )
• Relation Theory ( https://oeis.org/wiki/Relation_theory )
Regards,
Jon
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