Survey of Relation Theory

[Jon Awbrey]

Survey of Relation Theory
• https://inquiryintoinquiry.com/2023/07/26/survey-of-relation-theory-7/

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, focusing
on 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 Composition ( https://oeis.org/wiki/Relation_composition )
• Relation Construction ( https://oeis.org/wiki/Relation_construction )
• 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/

Information‑Theoretic Perspective (The Escape from Nominalism)

• Mathematical Demonstration and the Doctrine of Individuals

1. https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-1-2/

2. https://inquiryintoinquiry.com/2023/05/16/mathematical-demonstration-and-the-doctrine-of-individuals-2-2/

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