Re: [ontolog-forum] Relation Theory

Jon,

The structure which you describe as
[image: image.png]
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

[1] https://en.wikipedia.org/wiki/Algebraic_structure
[2] https://encyclopediaofmath.org/wiki/Algebraic_system
[3]
https://www.researchgate.net/publication/307841408_Finite_Systems_Handling_Language_YAFOLL_message_1


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

> 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
>
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