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Subject: [jvsw] Definition Edited At Word tseingu -- By krtisfranks
Date: Thu, 2 Aug 2018 23:39:16 -0700
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In jbovlaste, the user krtisfranks has edited a
definition of "tseingu" in the language "English".

Differences:

5,5c5,5
< 		While technically not good, this definition also employs the convention that $x_3$ is positive (countable) infinity if $A$ does not exist, meaning that $x_1$ and $x_2$ belong to mutually disjoint trees (or if at least one of them is undefined); in this case, $x_4$ is not well-defined (see: "{zi'au}"). This word can be used to specify the concept of "$n$th cousin $m$-times removed"-ness; $x_1$ and $x_2$ would be the cousins, $x_3-1 = n$, and $x_4$ is closely related to $m$ but is signed. If one views the tree graphs to which $x_1$ and $x_2$ belong with the viewing perspective such that siblings and spouses are mutually separated horizontally and such that ancestors are separated from their descendants vertically, then $x_3$ is the unsigned horizontal distance between $x_1$ and $x_2$. $x_4$ is, approximately, the signed generational offset/difference between subjects $x_1$ and $x_2$; it it their signed 'vertical' difference under the aforementioned viewing perspective. The relationship need not actually be cousinhood  (as perceived by English); direct ancestor-descendant pairs, (aunt/uncle)-(niece/nephew) pairs, and in fact any pair of family members with a well-specified most recent common ancestor (that is known) have this relationship to one another. This word can be used for specifying the number of "great"'s in the title of a relationship between $x_1$ and $x_2$ (with some calculational forethought). The tree diagram can be more generic than a family tree though; thus cousinhood is just a way to put it into context/application and is not really essential to the meaning except through analogy. Notice the ordering of all terms; if the graph is directed, the arguments of the distance matters. The graph should probably be a tree locally if it is to be a well-defined relationship. $x_3$ is unchanged but $x_4$ is negated (multiplied by $-1$) by/under exchange of $x_1$ and $x_2$. The ordered pair $(x_3, x_4)$ is named "consanguistance between $x_1$ and $x_2$ (in that order)" by Curtis Franks. For a normal family tree and fixed $x_1$ therein, consanguistance produces countably many equivalence classes of nodes. It does not recognize the difference between half or full relatives, marriages/parentings are either unsupported (when $x_3 > 0$) or are reduced to be equivalent (when $x_3 = 0$ and $x_4 \neq 0$), and gender/sex are ignored/reduced to equivalence. The set of nodes $x_2$ with $x_3 = 0$ is called $x_1$'s (the subject's) genealogical line (id est: if $x_3 = 0$, then $x_1$ re'au'e ja se dzena $x_2$ according to the edge relation on the graph or $x_1 = x_2$); the set of nodes with $x_3 > 0$ are sibling/branch/side lines, which could be labelled and ordered, but doing so would be somewhat difficult with this word. This word focuses on the relationship between $x_1$ and $x_2$, not the relationship between each of them and A; for that, see ".{anseingu}". The underlying tree graph is, modulo an equivalence relation involving tseingu, a 'quipyew' tree graph (see "{grafnkipliiu}"). This concept is fairly unnatural and convoluted, so it is probably {malgli} except for the purpose of translations; in a natural, culturally-neutral Lojbanic context, ".anseingu" is preferred.
---
> 		While technically not good, this definition also employs the convention that $x_3$ is positive (countable) infinity if $A$ does not exist, meaning that $x_1$ and $x_2$ belong to mutually disjoint trees (or if at least one of them is undefined); in this case, $x_4$ is not well-defined (see: "{zi'au}"). This word can be used to specify the concept of "$n$th cousin $m$-times removed"-ness; $x_1$ and $x_2$ would be the cousins, $x_3-1 = n$, and $x_4$ is closely related to $m$ but is signed. If one views the tree graphs to which $x_1$ and $x_2$ belong with the viewing perspective such that siblings and spouses are mutually separated horizontally and such that ancestors are separated from their descendants vertically (with ancestors in the positive direction relative to their descendants), then $x_3$ is the unsigned horizontal distance between $x_1$ and $x_2$. Additionally, $x_4$ is, approximately, the signed generational offset/difference between subjects $x_1$ and $x_2$; it is their signed 'vertical' difference under the aforementioned viewing perspective and sign convention. The relationship need not actually be cousinhood  (as perceived by English); direct ancestor-descendant pairs, (aunt/uncle)-(niece/nephew) pairs, and in fact any pair of family members with a well-specified most recent common ancestor (that is known) have this relationship to one another. This word can be used for specifying the number of "great"'s in the title of a relationship between $x_1$ and $x_2$ (with some calculational forethought). The tree diagram can be more generic than a family tree though; thus cousinhood is just a way to put it into context/application and is not really essential to the meaning except through analogy. Notice the ordering of all terms; if the graph is directed, the arguments of the distance matters. The graph should probably be a tree locally if it is to be a well-defined relationship. $x_3$ is unchanged but $x_4$ is negated (multiplied by $-1$) by/under exchange of $x_1$ and $x_2$. The ordered pair $(x_3, x_4)$ is named "consanguistance between $x_1$ and $x_2$ (in that order)" by Curtis Franks. For a normal family tree and fixed $x_1$ therein, consanguistance produces countably many equivalence classes of nodes. It does not recognize the difference between half or full relatives, marriages/parentings are either unsupported (when $x_3 > 0$) or are reduced to be equivalent (when $x_3 = 0$ and $x_4 \neq 0$), and gender/sex are ignored/reduced to equivalence. The set of nodes $x_2$ with $x_3 = 0$ is called $x_1$'s (the subject's) genealogical line (id est: if $x_3 = 0$, then $x_1$ re'au'e ja se dzena $x_2$ according to the edge relation on the graph or $x_1 = x_2$); the set of nodes with $x_3 > 0$ are sibling/branch/side lines, which could be labelled and ordered, but doing so would be somewhat difficult with this word. This word focuses on the relationship between $x_1$ and $x_2$, not the relationship between each of them and A; for that, see ".{anseingu}". The underlying tree graph is, modulo an equivalence relation involving tseingu, a 'quipyew' tree graph (see "{grafnkipliiu}"). This concept is fairly unnatural and convoluted, so it is probably {malgli} except for the purpose of translations; in a natural, culturally-neutral Lojbanic context, ".anseingu" is preferred.


Old Data:

	Definition:
		$x_1$ (node in a tree graph) and $x_2$ (node in the same tree graph) have an essentially unique most recent (graph-nearest) common ancestor node A such that $x_3$ [nonnegative integer; li] is the minimum element of the set consisting only of $d($A$, x_1)$ and of $d($A$, x_2)$, and such that $x_4$ [integer; li] is $d($A$, x_1) - d($A$, x_2)$, where $d$ is the graph geodesic distance (defined to be infinite if nodes are not connected in the correct direction).

	Notes:
		While technically not good, this definition also employs the convention that $x_3$ is positive (countable) infinity if $A$ does not exist, meaning that $x_1$ and $x_2$ belong to mutually disjoint trees (or if at least one of them is undefined); in this case, $x_4$ is not well-defined (see: "{zi'au}"). This word can be used to specify the concept of "$n$th cousin $m$-times removed"-ness; $x_1$ and $x_2$ would be the cousins, $x_3-1 = n$, and $x_4$ is closely related to $m$ but is signed. If one views the tree graphs to which $x_1$ and $x_2$ belong with the viewing perspective such that siblings and spouses are mutually separated horizontally and such that ancestors are separated from their descendants vertically, then $x_3$ is the unsigned horizontal distance between $x_1$ and $x_2$. $x_4$ is, approximately, the signed generational offset/difference between subjects $x_1$ and $x_2$; it it their signed 'vertical' difference under the aforementioned viewing perspective. The relationship need not actually be cousinhood  (as perceived by English); direct ancestor-descendant pairs, (aunt/uncle)-(niece/nephew) pairs, and in fact any pair of family members with a well-specified most recent common ancestor (that is known) have this relationship to one another. This word can be used for specifying the number of "great"'s in the title of a relationship between $x_1$ and $x_2$ (with some calculational forethought). The tree diagram can be more generic than a family tree though; thus cousinhood is just a way to put it into context/application and is not really essential to the meaning except through analogy. Notice the ordering of all terms; if the graph is directed, the arguments of the distance matters. The graph should probably be a tree locally if it is to be a well-defined relationship. $x_3$ is unchanged but $x_4$ is negated (multiplied by $-1$) by/under exchange of $x_1$ and $x_2$. The ordered pair $(x_3, x_4)$ is named "consanguistance between $x_1$ and $x_2$ (in that order)" by Curtis Franks. For a normal family tree and fixed $x_1$ therein, consanguistance produces countably many equivalence classes of nodes. It does not recognize the difference between half or full relatives, marriages/parentings are either unsupported (when $x_3 > 0$) or are reduced to be equivalent (when $x_3 = 0$ and $x_4 \neq 0$), and gender/sex are ignored/reduced to equivalence. The set of nodes $x_2$ with $x_3 = 0$ is called $x_1$'s (the subject's) genealogical line (id est: if $x_3 = 0$, then $x_1$ re'au'e ja se dzena $x_2$ according to the edge relation on the graph or $x_1 = x_2$); the set of nodes with $x_3 > 0$ are sibling/branch/side lines, which could be labelled and ordered, but doing so would be somewhat difficult with this word. This word focuses on the relationship between $x_1$ and $x_2$, not the relationship between each of them and A; for that, see ".{anseingu}". The underlying tree graph is, modulo an equivalence relation involving tseingu, a 'quipyew' tree graph (see "{grafnkipliiu}"). This concept is fairly unnatural and convoluted, so it is probably {malgli} except for the purpose of translations; in a natural, culturally-neutral Lojbanic context, ".anseingu" is preferred.

	Jargon:
		

	Gloss Keywords:
		Word: consanguinity values, In Sense: 
		Word: consanguistance, In Sense: C. Franks' neologism, genealogy
		Word: cousin degree, In Sense: 
		Word: cousin order, In Sense: ordinal of cousin relationship
		Word: cousin removal, In Sense: 
		Word: degree of removal, In Sense: cousin relationship
		Word: kinship number, In Sense: 

	Place Keywords:


New Data:

	Definition:
		$x_1$ (node in a tree graph) and $x_2$ (node in the same tree graph) have an essentially unique most recent (graph-nearest) common ancestor node A such that $x_3$ [nonnegative integer; li] is the minimum element of the set consisting only of $d($A$, x_1)$ and of $d($A$, x_2)$, and such that $x_4$ [integer; li] is $d($A$, x_1) - d($A$, x_2)$, where $d$ is the graph geodesic distance (defined to be infinite if nodes are not connected in the correct direction).

	Notes:
		While technically not good, this definition also employs the convention that $x_3$ is positive (countable) infinity if $A$ does not exist, meaning that $x_1$ and $x_2$ belong to mutually disjoint trees (or if at least one of them is undefined); in this case, $x_4$ is not well-defined (see: "{zi'au}"). This word can be used to specify the concept of "$n$th cousin $m$-times removed"-ness; $x_1$ and $x_2$ would be the cousins, $x_3-1 = n$, and $x_4$ is closely related to $m$ but is signed. If one views the tree graphs to which $x_1$ and $x_2$ belong with the viewing perspective such that siblings and spouses are mutually separated horizontally and such that ancestors are separated from their descendants vertically (with ancestors in the positive direction relative to their descendants), then $x_3$ is the unsigned horizontal distance between $x_1$ and $x_2$. Additionally, $x_4$ is, approximately, the signed generational offset/difference between subjects $x_1$ and $x_2$; it is their signed 'vertical' difference under the aforementioned viewing perspective and sign convention. The relationship need not actually be cousinhood  (as perceived by English); direct ancestor-descendant pairs, (aunt/uncle)-(niece/nephew) pairs, and in fact any pair of family members with a well-specified most recent common ancestor (that is known) have this relationship to one another. This word can be used for specifying the number of "great"'s in the title of a relationship between $x_1$ and $x_2$ (with some calculational forethought). The tree diagram can be more generic than a family tree though; thus cousinhood is just a way to put it into context/application and is not really essential to the meaning except through analogy. Notice the ordering of all terms; if the graph is directed, the arguments of the distance matters. The graph should probably be a tree locally if it is to be a well-defined relationship. $x_3$ is unchanged but $x_4$ is negated (multiplied by $-1$) by/under exchange of $x_1$ and $x_2$. The ordered pair $(x_3, x_4)$ is named "consanguistance between $x_1$ and $x_2$ (in that order)" by Curtis Franks. For a normal family tree and fixed $x_1$ therein, consanguistance produces countably many equivalence classes of nodes. It does not recognize the difference between half or full relatives, marriages/parentings are either unsupported (when $x_3 > 0$) or are reduced to be equivalent (when $x_3 = 0$ and $x_4 \neq 0$), and gender/sex are ignored/reduced to equivalence. The set of nodes $x_2$ with $x_3 = 0$ is called $x_1$'s (the subject's) genealogical line (id est: if $x_3 = 0$, then $x_1$ re'au'e ja se dzena $x_2$ according to the edge relation on the graph or $x_1 = x_2$); the set of nodes with $x_3 > 0$ are sibling/branch/side lines, which could be labelled and ordered, but doing so would be somewhat difficult with this word. This word focuses on the relationship between $x_1$ and $x_2$, not the relationship between each of them and A; for that, see ".{anseingu}". The underlying tree graph is, modulo an equivalence relation involving tseingu, a 'quipyew' tree graph (see "{grafnkipliiu}"). This concept is fairly unnatural and convoluted, so it is probably {malgli} except for the purpose of translations; in a natural, culturally-neutral Lojbanic context, ".anseingu" is preferred.

	Jargon:
		

	Gloss Keywords:
		Word: consanguinity values, In Sense: 
		Word: consanguistance, In Sense: C. Franks' neologism, genealogy
		Word: cousin degree, In Sense: 
		Word: cousin order, In Sense: ordinal of cousin relationship
		Word: cousin removal, In Sense: 
		Word: degree of removal, In Sense: cousin relationship
		Word: kinship number, In Sense: 

	Place Keywords:


You can go to <http://jbovlaste.lojban.org/dict/tseingu> to see it.