# Relation Theory

47 views

### Jon Awbrey

Apr 16, 2023, 11:01:07 AMApr 16
to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG, RDF Surfaces (Public), RDF Surfaces
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.

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 )
• 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

Peirce's 1870 “Logic of Relatives” —

Overview
https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-overview/

Preliminaries
https://inquiryintoinquiry.com/2014/01/27/peirces-1870-logic-of-relatives-preliminaries/

Regards,

Jon

### Ravi Sharma

Apr 17, 2023, 4:25:03 AMApr 17
to ontolo...@googlegroups.com, Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG, RDF Surfaces (Public), RDF Surfaces
Jon
Is there also an attempt at integrating these relation concepts? like a meta-model of relations?
Thanks.
Ravi
(Dr. Ravi Sharma, Ph.D. USA)
NASA Apollo Achievement Award
Chair, Ontology Summit 2022
Particle and Space Physics
Senior Enterprise Architect

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### Jon Awbrey

Apr 19, 2023, 4:48:52 PMApr 19
to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG, RDF Surfaces (Public)
Cf: Relation Theory • Discussion 4
https://inquiryintoinquiry.com/2023/04/19/relation-theory-discussion-4/

Re: Survey of Relation Theory
https://inquiryintoinquiry.com/2023/04/01/survey-of-relation-theory-6/
Re: Ontolog Forum
::: Ravi Sharma

<QUOTE RS:>
Is there also an attempt at integrating these relation concepts?
Like a meta-model of relations?
</QUOTE>

Dear Ravi,

Thanks for the question. I believe I'd say yes to the
first part, since integrating diverse concepts is a big
part of what's called for here. At any rate, if we are
taking about the list of Relational Concepts at the top
of the above Survey Page then those are just so many
facets exhibited by the family of mathematical objects
known as relations.

Regards,

Jon

### Alex Shkotin

Apr 20, 2023, 5:05:53 AMApr 20
to ontolo...@googlegroups.com, Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG, RDF Surfaces (Public), RDF Surfaces
Jon,

The structure which you describe as

reminds me of my favorite structure "algebraic system", where we call every Xi the underlying set, carrier set or domain [1].
So you introduced a multi-carrier algebraic system with one relation in it.
As they call "relation" [2] the subset of the cartesian product which you call "graph".
The algebraic system you describe is called relational as there are no operations in it.
Let me issue a hypothesis that any result in your Relations theory may be reformulated as a result in the theory of algebraic systems:-)
By the way, my experimental language YAFOLL is primarily to work with finite many-domain (aka sorts) algebraic systems [3].

One world, a lot of views:-)

Best regards,

Alex

вс, 16 апр. 2023 г. в 18:01, Jon Awbrey <jaw...@att.net>:

### Jon Awbrey

Apr 22, 2023, 1:00:07 PMApr 22
to Cybernetic Communications, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Relation Theory • Discussion 5
https://inquiryintoinquiry.com/2023/04/22/relation-theory-discussion-5/

Re: Survey of Relation Theory
https://inquiryintoinquiry.com/2023/04/01/survey-of-relation-theory-6/
Re: Ontolog Forum
::: Ravi Sharma

<QUOTE RS:>
Is there also an attempt at integrating these relation concepts?
Like a meta‑model of relations?
</QUOTE>

Dear Ravi,

For the rest of your question, I haven't run across the concept
of a meta‑model before so I wasn't sure about that. If you get
a chance, maybe you can tell me more about that.

Many past discussions of models and their theories tell me a thicket of
failures to communicate is almost bound to arise at this point. One or
two pieces I've written in the past lay out the landscape a lot better
than I'm likely to do off the cuff, so I'll go look those up, but also
see if I can find a fresh perspective on the scene.

Regards,

Jon (https://mathstodon.xyz/@Inquiry)