관계,relation

Difference between r1.41 and the current

@@ -413,6 +413,7 @@
[[relevance]] =,relevance . relevance
{
연관성, 적절한 정도, ... 지금 상황에 맞는지 여부를 따지는 그런 뉘앙스가 포함된 듯 한데
관련성?

WtEn:relevance
NdEn:relevance

Sub:



semantic_relation =,semantic_relation . semantic_relation
semantic relation
https://www.gabormelli.com/RKB/Semantic_Relation
aka conceptual relation. conceptual_relation =,conceptual_relation Ggl:conceptual relation
// semantic relation Ggl:semantic relation

word_sense_relation =,word_sense_relation . word_sense_relation
lexical_relation =,lexical_relation . lexical_relation
word sense relation
lexical relation
https://www.gabormelli.com/RKB/Word_Sense_Relation (Redirected from lexical relation)
// word sense relation Ggl:word sense relation
// lexical relation Ggl:lexical relation

...tbw

}

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1. Def.

정의:
집합,set(들)의 cartesian product(곱집합,product_set)의 부분집합,subset. (mw)
그러니까 이렇게 정의해야 2-relation 말고도 1 3 4 5 ....로 일반화가능한거지? 근데 nullary relation은 그럼? chk Ggl:nullary relation definition ...
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2. Sub:

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2.1. (operand?의 개수? arity? 기준으로) 0, 1, 2, ....

// 일단 degree(curr 디그리,degree) / arity(arity) / 대상 집합들의 개수 / .... 기준으로

0인 경우도 존재.
https://en.wikipedia.org/wiki/Relation_of_degree_zero
"relation of degree zero, 0-ary relation, or nullary relation"
// arity / 디그리,degree / 영,zero

1 unary_relation ?

2 이항관계,binary_relation
동치관계,equivalence_relation -> VG:동치관계,equivalence_relation

3, 4, ...
일반적 명칭? - Ggl:n-ary relation 해보니 나오긴 하는데
QQQ 'k-adic relation' 과 같은 거? ( logical_matrix 언급에서. https://oeis.org/wiki/Logical_matrix )
cf.

(misc delme) 철자 혼동 주의: 이하 (in)finitiary 가 아니라 (in)finitary 임

(유한한 수)
finitary_relation =,finitary_relation . finitary_relation
{
finitary relation
https://www.gabormelli.com/RKB/Finitary_Relation
WpEn:Finitary_relation
WtEn:finitary_relation x 2023-08-22
} // finitary relation ... Ggl:finitary relation

그럼 infinitary_relation 라는 것도 존재? QQQ
∞ infinitary_relation
infinitary relation
...
ndict x 2023-08-22
Naver:infinitary relation
Bing:infinitary relation
Google:infinitary relation
https://en.wikipedia.org/wiki/Infinitary_relation - doesn't exist - 2023-08-22
별도 항목으로 따로 둔 사전/백과/위키는 없는 듯 하고 대개 finitary_relation 에서 같이 설명함.
See:
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Cool_Brisk_Walk_Through_Discrete_Mathematics_(Davies)/03:_Relations/3.4:_Finite_and_infinite_relations
직접 관련된건 아니지만 see also:
https://en.wikipedia.org/wiki/Infinitary_combinatorics
rel:
무한집합,infinite_set
"infinitary relation"

-1, -2, ..., 유리수, 실수 이런건 meaningless? cardinal_number에만 의미있음? or expandable?

....

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2.2. inverse relation

inverse_relation =,inverse_relation . inverse_relation
inverse relation
인버스관계
역관계 ?


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2.3. satisfaction relation

satisfaction_relation =,satisfaction_relation . satisfaction_relation
{
satisfaction relation

REL
satisfaction =,satisfaction . satisfaction {


만족

이것보다 관련표현인 satisfiability 가 매우 자주 보인다... 아래.

관련표현
satisfactory adj. 만족스러운
satisfiability n. - 보통 '충족가능성'으로 번역하는 게 대세인듯. // or 충족여부 만족가능성 만족여부 ?? // =,satisfiability =,satisfiability . satisfiability
KmsE:satisfiability x 2023-08-25
WtEn:satisfiability = https://en.wiktionary.org/wiki/satisfiability
https://en.wikipedia.org/wiki/Satisfiability
esp Boolean_satisfiability Boolean satisfiability (이걸 줄여서 SAT ?)
satisfiability_problem =,satisfiability_problem . satisfiability_problem
satisfiability problem (이걸 줄여서 SAT ?)
rel conjunctive_normal 논리곱 정규형 ..
Sub
2-SAT
3-SAT
4-SAT etc
the first known NP-complete problem (Stephen_Cook 1971)
https://mathworld.wolfram.com/Satisfaction.html
}


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2.4. one-to-many relation

one-to-many_relation =,one-to-many_relation . one-to-many_relation
{
one-to-many relation
일대다 관계 ?


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2.5. many-to-one relation

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2.6. many-to-many relation

many-to-many_relation =,many-to-many_relation . many-to-many_relation
{
many-to-many relation
다대다 관계?


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2.7. relational structure

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2.8. homogeneous relation / endorelation

homogeneous_relation =,homogeneous_relation . homogeneous_relation
endorelation =,endorelation . endorelation
{
homogeneous relation
AKA
endorelation

"on a set X is a binary_relation between X and itself" (we)
즉 동일 집합간 이항관계,binary_relation - cartesian product $\displaystyle X\times X$ 의 subset.



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2.9. symmetric relation

symmetric_relation =,symmetric_relation =,symmetric_relation . symmetric_relation
symmetric relation
WtEn:symmetric_relation x(2023-08-15)
https://en.wikipedia.org/wiki/Symmetric_relation
symmetric relation
대칭관계 ?
KmsE:symmetric relation
Ggl:symmetric relation
"symmetric relation"
Up: 대칭성,symmetry


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2.10. relation symbol

relation_symbol =,relation_symbol =,relation_symbol . relation_symbol
{
relation symbol
aka: = predicate_symbol = predicate_letter



Bing:relation symbol
Ggl:relation symbol
"relation symbol"
}


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2.11. reflection relation

reflection_relation =,reflection_relation =,reflection_relation . reflection_relation
{
반사관계? -
reflection relation




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2.12. translation relation

translation_relation =,translation_relation =,translation_relation . translation_relation
{
translation relation



"translation relation"
}


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2.13. recurrence relation

recurrence_relation =,recurrence_relation =,recurrence_relation . recurrence_relation
{
recurrence relation


https://mathworld.wolfram.com/RecurrenceRelation.html
REL
"When ..., known as recurrence_equation { https://mathworld.wolfram.com/RecurrenceEquation.html } s, or sometimes difference_equation s"
(VG: 점화식,recurrence_relation exists (VG:점화식,recurrence_relation) .... 다만 페이지를 점화관계,recurrence_relation recurrence_equation로 나눌 생각을 나도 하는 중.)
}

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2.14. universal relation

universal_relation =,universal_relation . universal_relation
{
universal relation


"universal relation"
}

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2.15. total relation

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2.16. closure relation

closure_relation =,closure_relation . closure_relation
{
closure relation
https://mathworld.wolfram.com/ClosureRelation.html
WtEn:closure_relation x
"closure relation"
}

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2.17. transitive relation

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2.18. antireflexive relation

aka antireflective_relation ?? chk Ggl:antireflexive relation antireflexive relation
antireflexive_relation =,antireflexive_relation =,antireflexive_relation . antireflexive_relation
{
antireflexive relation

https://proofwiki.org/wiki/Definition:Antireflexive_Relation
irreflexive 표현을 쓸 때도 있는데, non-reflexive와 혼동 가능하므로,
WtEn:antireflexive_relation
WpEn:Antireflexive_relation


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2.19. sign relation

sign_relation =,sign_relation =,sign_relation . sign_relation
{
sign relation







"sign relation"
}

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2.20. finitary relation

finitary relation

finitary_relation


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2.21. ADDHERE

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2.22. ADDHERE

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2.23. ADDHERE

..... ADDHERE ......

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3. 분야: relation theory ? relational theory ?

relation theory
"relation theory"

Up:
relation_theory =,relation_theory . relation_theory
{
관계론 관계이론
WtEn:relation_theory
KmsE:relation



... aka relational_theory ?
2023-08-15:
WpEn:Relational_theory - No, [https]nlab에서 여기로 링크했으나 아님.
WpEn:Relation_theory - 페이지없음.

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4. MKLINK

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4.1. arity

arity =,arity . arity
{
WpEn:Arity - "is the number of arguments or operands taken by a function, operation or relation" 즉 함수,function 펑션,function 연산,operation 관계,relation가 가지는 성질. 자료구조,data_structure or ADT : 배열,array등도?

0 nullary
1 unary
2 binary
3 ternary https://www.gabormelli.com/RKB/Ternary_Relation
일반적으로 n-ary


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5. 비슷? cmp.

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5.1. relation vs correspondence

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5.2. relation vs relevance

relevance =,relevance . relevance
{
연관성, 적절한 정도, ... 지금 상황에 맞는지 여부를 따지는 그런 뉘앙스가 포함된 듯 한데
관련성?


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5.3. relation vs association

연관,association
'관계있는 것'과 '연관짓는 것'의 차이를 명확히 서술? 을 할까말까?
생각을 해보아야.. 아주 대충만 생각해보면, 어떤 주체subject가 '연관짓는 행동'을 한다면, 그 두 대상은 '관계있는 것'일 가능성,possibility이 높다.

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6. TAIL

관계,relation Modified on 12:53 am, August 28, 2024.
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