List,
Loet Leydesdorff included PEIRCE-L among recipients of the following
message, but the message was held by the PEIRCE-L server in moderation,
since Mr. Leydesdorff is not subscribed to PEIRCE-L. I contacted him
and asked about his maybe joining the list or my maybe forwarding to the
list, and he replied: "I would be most grateful if you could forward.
I am not sufficiently involved in this issue to follow all the
discussions. I reacted on a contribution in a parallel list."
Best regards,
Ben Udell, co-manager with moderator Gary Richmond
PEIRCE-L
To: [email protected], "Cybernetic Communications"
<[email protected]>, "Ontolog Forum"
<[email protected]>, "Peirce List"
<[email protected]>, "Structural Modeling"
<[email protected]>, SysSciWG <[email protected]>
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
You may find it interesting.
Best,
Loet
Loet Leydesdorff
Professor emeritus, University of Amsterdam
Amsterdam School of Communication Research (ASCoR)
[email protected] ; http://www.leydesdorff.net/
Associate Faculty, SPRU, University of Sussex;
Guest Professor Zhejiang Univ., Hangzhou; Visiting Professor, ISTIC,
Beijing;
Visiting Fellow, Birkbeck, 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
[....]
To view this discussion on the web visit
https://groups.google.com/d/msgid/cybcom/a3de28e4-dd9e-5c11-aee6-b63915b2a097%40att.net.
Subject:
Re: [CYBCOM] Re: Triadic Relations
From:
"Loet Leydesdorff" <[email protected]>
Date:
5/23/2020, 9:18 AM
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