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Apr 16, 2023, 11:01:07 AM4/16/23

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.

Please follow the above link for the full set of resources.

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 )

• Triadic Relation ( https://oeis.org/wiki/Triadic_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

• https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-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

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.

Please follow the above link for the full set of resources.

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 )

• Triadic Relation ( https://oeis.org/wiki/Triadic_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

• https://inquiryintoinquiry.com/2015/02/04/six-ways-of-looking-at-a-triadic-relation-%E2%8C%AC-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

Apr 17, 2023, 4:25:03 AM4/17/23

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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Apr 19, 2023, 4:48:52 PM4/19/23

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

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8

::: Ravi Sharma

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8/m/FWbax8syCAAJ

<QUOTE RS:>

</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

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

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8

::: Ravi Sharma

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8/m/FWbax8syCAAJ

<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

Apr 20, 2023, 5:05:53 AM4/20/23

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

[3] https://www.researchgate.net/publication/307841408_Finite_Systems_Handling_Language_YAFOLL_message_1

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

Apr 22, 2023, 1:00:07 PM4/22/23

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

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8

::: Ravi Sharma

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8/m/FWbax8syCAAJ

<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)

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

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8

::: Ravi Sharma

https://groups.google.com/g/ontolog-forum/c/vlbILmZMsJ8/m/FWbax8syCAAJ

<QUOTE RS:>

Is there also an attempt at integrating these relation concepts?

</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)

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