Difference between revisions of "BPFK Section: Non-logical Connectives"

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(Proposed Definition: {pi'u}: Replacing another occurrence of "cross product" with "Cartesian product".)
 
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{{BPFK Section from tiki|BPFK Section: Non-logical Connectives|22}}
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==Proposed definitions ==
  
== Proposed definitions ==
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{{BPFK Section box open}}
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=== cmavo: jo'u (JOI) ===
  
 +
==== Proposed Definition ====
 +
And. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly. More than two sumti may be joined into one sumti by chaining up additional { jo'u ''SUMTI'' }.
  
=== jo'u (JOI) ===
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==== See Also ====
  
==== Definition ====
+
==== Proposed Keywords ====
 
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* and
And. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly.
 
 
 
==== Keywords ====
 
 
 
* And
 
 
 
==== Examples ====
 
  
 +
==== Usage Examples ====
 
;.i mi jo'u la .clsn. cu ciksi tu'a lo cmavo be zo coi:''Me and Shoulson are explaining about the cmavo of selma'o COI.''
 
;.i mi jo'u la .clsn. cu ciksi tu'a lo cmavo be zo coi:''Me and Shoulson are explaining about the cmavo of selma'o COI.''
  
 
;lo za'e tridu cu mixre lo tricu jo'u lo tcidu:''A 'treeder' is a mixture of a tree and a reader.''
 
;lo za'e tridu cu mixre lo tricu jo'u lo tcidu:''A 'treeder' is a mixture of a tree and a reader.''
 +
{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
 
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=== cmavo: ju'e (JOI) ===
 
 
=== ju'e (JOI) ===
 
 
 
==== Definition ====
 
 
 
Vague connective. Joins two sumti into one sumti. The referent of the resulting sumti is some function of the referents of both sumti.
 
  
==== Keywords ====
+
==== Proposed Definition ====
 +
Vague connective. Joins two sumti into one sumti. The referent of the resulting sumti is some function of the referents of both sumti. More than two sumti may be joined into one sumti by chaining up additional { ju'e ''SUMTI'' }.
  
*Vague connective
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==== See Also ====
  
==== Examples ====
+
==== Proposed Keywords ====
 +
* vague connective
  
 +
==== Usage Examples ====
 
;mi'a casnu zo jetnu ju'e zo fatci ju'e lo si'o jetnu ku ju'e lo si'o fatci:''We are discussing about "truth"/"fact"/truth/fact.'' (IRC, Eimi, 22 Dec 2008 07:40:19)
 
;mi'a casnu zo jetnu ju'e zo fatci ju'e lo si'o jetnu ku ju'e lo si'o fatci:''We are discussing about "truth"/"fact"/truth/fact.'' (IRC, Eimi, 22 Dec 2008 07:40:19)
  
:.i ji'a co'e lo plise ju'e lo perli ju'e lo drata:''Also an apple and a pear.'' (IRC, xalbo, 5 Oct 2010 12:50:22)
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;.i ji'a co'e lo plise ju'e lo perli ju'e lo drata:''Also an apple and a pear.'' (IRC, xalbo, 5 Oct 2010 12:50:22)
 
 
{BOX}
 
 
 
  
===  fa'u (JOI) ===
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{{BPFK Section box close}}
  
==== Definition ====
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{{BPFK Section box open}}
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=== cmavo: fa'u (JOI) ===
  
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==== Proposed Definition ====
 
Respectively. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly and distributively in correspondence with another term.
 
Respectively. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly and distributively in correspondence with another term.
  
==== Keywords ====
+
==== See Also ====
  
*Respectively
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==== Proposed Keywords ====
 
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* respectively
==== Examples ====
 
  
 +
==== Usage Examples ====
 
;mi fa'u do klama lo zdani fa'u lo zarci:''Me and you go home and to the market, respectively.''
 
;mi fa'u do klama lo zdani fa'u lo zarci:''Me and you go home and to the market, respectively.''
  
 
;li pano fa'u li cinono cu jdima lo nu klama fu lo girzu karce fa'u lo vinji:''Ten and three-hundred are the prices of going by bus and by plane, respectively.''
 
;li pano fa'u li cinono cu jdima lo nu klama fu lo girzu karce fa'u lo vinji:''Ten and three-hundred are the prices of going by bus and by plane, respectively.''
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{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
 
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=== cmavo: joi (JOI) ===
 
 
=== joi (JOI) ===
 
 
 
==== Definition ====
 
 
 
Non-distributive group. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly and non-distributively.
 
 
 
==== Keywords ====
 
  
* Both
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==== Proposed Definition ====
* Together with
+
Non-distributive group. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly and non-distributively. More than two sumti may be joined into one sumti by chaining up additional { joi ''SUMTI'' }.
  
* And
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==== See Also ====
 +
* {gunma}
  
==== Example ====
+
==== Proposed Keywords ====
 +
* both
 +
* together with
 +
* and
  
 +
==== Usage Example ====
 
;mi joi ry. ze'a casnu lo lijda ctuca tadji:''Me and R have been discussing religious teaching methods.''
 
;mi joi ry. ze'a casnu lo lijda ctuca tadji:''Me and R have been discussing religious teaching methods.''
  
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;la jegvon cu cevni le xriso joi le xebro joi le muslo:''Jehovah is the god of the Christians, the Jews and the Muslims.''
 
;la jegvon cu cevni le xriso joi le xebro joi le muslo:''Jehovah is the god of the Christians, the Jews and the Muslims.''
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{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
 
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=== cmavo: ce (JOI) ===
  
=== ce (JOI) ===
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==== Proposed Definition ====
 +
Joins two sumti into one sumti. The referent of the resulting sumti is the set whose members are the referents of both sumti considered jointly. More than two sumti may be joined into one sumti by chaining up additional { ce ''SUMTI'' }. Thus, {X ce Y ce Z} creates one single set containing X, Y and Z.
  
==== Definition ====
+
==== See Also ====
 +
* {cmima}
  
Joins two sumti into one sumti. The referent of the resulting sumti is the set whose members are the referents of both sumti considered jointly.
+
==== Proposed Keywords ====
 
+
* and (set)
==== Keywords ====
 
 
 
* And (set)
 
 
 
==== Examples ====
 
  
 +
==== Usage Examples ====
 
;.abu ce by ce cy vasru .abu ce by:''{a, b, c} ⊇ {a, b}''
 
;.abu ce by ce cy vasru .abu ce by:''{a, b, c} ⊇ {a, b}''
 +
{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
 
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=== cmavo: ce'o (JOI) ===
 
 
=== ce'o (JOI) ===
 
 
 
==== Definition ====
 
 
 
Joins two sumti into one sumti. The referent of the resulting sumti is the sequence whose members are the referents of both sumti considered jointly.
 
  
==== Keywords ====
+
==== Proposed Definition ====
 +
Joins two sumti into one sumti. The referent of the resulting sumti is the sequence whose members are the referents of both sumti considered jointly. More than two sumti may be joined into one sumti by chaining up additional { ce'o ''SUMTI'' }.
  
* And (sequence)
+
==== See Also ====
 +
* {porsi}
  
==== Examples ====
+
==== Proposed Keywords ====
 +
* and (sequence)
  
 +
==== Usage Examples ====
 
;jukpa ce'o citka lo cersai co'o ru'e:''Making and eating breakfast, bye for now.''
 
;jukpa ce'o citka lo cersai co'o ru'e:''Making and eating breakfast, bye for now.''
  
 
;.abu ce'o by cu mleca cy ce'u dy .ijo ge .abu mleca cy gi by mleca dy:''(a,b) ≤ (c,d) if and only if a ≤ c and b ≤ d''
 
;.abu ce'o by cu mleca cy ce'u dy .ijo ge .abu mleca cy gi by mleca dy:''(a,b) ≤ (c,d) if and only if a ≤ c and b ≤ d''
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{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
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=== cmavo: jo'e (JOI) ===
  
 +
==== Proposed Definition ====
 +
Union of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the union of the sets referred to by each sumti. More than two sumti may be joined into one sumti by chaining up additional { jo'e ''SUMTI'' }.
  
=== jo'e (JOI) ===
+
==== See Also ====
  
==== Definition ====
+
==== Proposed Keywords ====
 
+
* union
Union of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the union of the sets referred to by each sumti.
 
 
 
==== Keywords ====
 
 
 
* Union
 
 
 
==== Examples ====
 
  
 +
==== Usage Examples ====
 
;lo'i brivla cu du lo'i gismu jo'e lo'i fu'ivla jo'e lo'i lujvo to po'o xu toi:''The set of brivla is equal to the union of the set of gismu and the set of fu'ivla and the set of lujvo (only?).''
 
;lo'i brivla cu du lo'i gismu jo'e lo'i fu'ivla jo'e lo'i lujvo to po'o xu toi:''The set of brivla is equal to the union of the set of gismu and the set of fu'ivla and the set of lujvo (only?).''
 +
{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
 +
=== cmavo: ku'a (JOI) ===
  
 +
==== Proposed Definition ====
 +
Intersection of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the intersection of the sets referred to by each sumti. More than two sumti may be joined into one sumti by chaining up additional { ku'a ''SUMTI'' }.
  
=== ku'a (JOI) ===
+
==== See Also ====
 
 
==== Definition ====
 
 
 
Intersection of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the intersection of the sets referred to by each sumti.
 
 
 
==== Keywords ====
 
  
 +
==== Proposed Keywords ====
 
*Intersection
 
*Intersection
  
==== Examples ====
+
==== Usage Examples ====
 
 
 
;xy cmima .abu ku'a by .ijo ge xy cmima .abu gi xy cmima by:''x ∈ A ∩ B if and only if x ∈ A and x ∈ B.''
 
;xy cmima .abu ku'a by .ijo ge xy cmima .abu gi xy cmima by:''x ∈ A ∩ B if and only if x ∈ A and x ∈ B.''
 +
{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
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=== cmavo: pi'u (JOI) ===
  
 +
==== Proposed Definition ====
 +
Cartesian product of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the Cartesian product of the sets referred to by each sumti.
  
=== pi'u (JOI) ===
+
==== See Also ====
 
 
==== Definition ====
 
 
 
Cross product of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the cross product of the sets referred to by each sumti.
 
 
 
==== Keywords ====
 
  
 +
==== Proposed Keywords ====
 +
* Cartesian Product
 
* Set Product
 
* Set Product
* Cartesian Product
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* Cross product
 
 
==== Examples ====
 
  
 +
==== Usage Examples ====
 +
;ko cuxna lo sanmi pi'u gi lo ckafi ce lo tcati gi lo grute ce lo nanba
 +
:''Choose a meal from the Cartesian product of the set {coffee, tea} and the set {fruits, bread}.''
 +
:''For the meal, choose one of coffee or tea, and one of fruits or bread.''
 
;le'i bebna ku pi'u le'i mabla sidbo ku cu barda:''The cross product of the set of silly things and the set of bad ideas is large.''
 
;le'i bebna ku pi'u le'i mabla sidbo ku cu barda:''The cross product of the set of silly things and the set of bad ideas is large.''
 +
{{BPFK Section box close}}
  
{BOX}
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{{BPFK Section box open}}
 
 
 
=== Formal definitions ===
 
=== Formal definitions ===
  
||
+
{| class="wikitable"
 
+
| '''X''' ju'e '''Y''' || = lo co'e be '''X''' bei '''Y'''
''sumti1'' JOI ''sumti2''
+
|-
 
+
| '''X''' jo'u '''Y''' || = lo suzmei noi ge '''X''' .e '''Y''' me ke'a gi ro me ke'a cu me '''X''' gi'a me '''Y'''
ge ''sumti1'' gi ''sumti2'' me ''sumti1'' jo'u ''sumti2''
+
|-
 
+
| '''X''' joi '''Y''' || = lo gunma be '''X''' .e '''Y'''
''sumti1'' ju'e ''sumti2'' | lo co'e be ''sumti1'' bei ''sumti2''
+
|-
 
+
| '''X''' ce '''Y''' || = lo se cmima be '''X''' .e '''Y''' .e no drata be '''X''' .e '''Y'''
''sumti1'' jo'u ''sumti2'' | lo sumji be ''sumti1'' bei ''sumti2''
+
|-
 
+
| '''X''' ce'o '''Y''' || = lo porsi be fi '''X''' jo'u '''Y''' be'o noi '''X''' lidne '''Y''' ke'a
''sumti1'' jo'e ''sumti2'' | lo jomsumji be ''sumti1'' bei ''sumti2''
+
|-
 
+
| '''X''' jo'e '''Y''' || = lo selcmi noi ro cmima be ke'a cu cmima '''X''' .a '''Y'''
''sumti1'' ku'a ''sumti2'' | lo kuzyterkruca be ''sumti1'' bei ''sumti2''
+
|-
 
+
| '''X''' ku'a '''Y''' || = lo selcmi noi ro cmima be ke'a cu cmima '''X''' .e '''Y'''
''sumti1'' pi'u ''sumti2'' | lo pivypilji be ''sumti1'' bei ''sumti2''
+
|-
 
+
| '''X''' pi'u '''Y''' || = lo selcmipi'i be '''X''' bei '''Y'''
''sumti1'' jo'u ''sumti2'' | lu'a ''sumti1'' jo'u ''sumti2''
+
|-
 
+
|colspan=1| ''sumti1'' fa'u ''sumti2'' ''sumti3'' fa'u ''sumti4'' ''selbri'' == ''sumti1'' ''sumti3'' ''selbri'' .i ''sumti2'' ''sumti4'' ''selbri''
''sumti1'' joi ''sumti2'' | lu'o ''sumti1'' jo'u ''sumti2''
+
|}
 
 
''sumti1'' ce ''sumti2'' | lu'i ''sumti1'' jo'u ''sumti2''
 
 
 
''sumti1'' ce'o ''sumti2'' | vu'i ''sumti1'' jo'u ''sumti2''
 
 
 
''sumti1'' fa'u ''sumti2'' ''sumti3'' fa'u ''sumti4'' ''selbri''
 
 
 
== ''sumti1'' ''sumti3'' ''selbri'' .i ''sumti2'' ''sumti4'' ''selbri''
 
 
 
||
 
  
 
=== Notes ===
 
=== Notes ===
 +
# The definitions given correspond to their use as sumti connectives. Other uses (when they make sense) have yet to be added.
  
# The definitions given correspond to their use as sumti connectives. Other uses (when they make sense) have yet to be added.
+
=== Impact ===

Latest revision as of 14:14, 2 April 2016

This page is imported from version 22 of the page BPFK Section: Non-logical Connectives from the lojban Tiki.

Proposed definitions

cmavo: jo'u (JOI)

Proposed Definition

And. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly. More than two sumti may be joined into one sumti by chaining up additional { jo'u SUMTI }.

See Also

Proposed Keywords

  • and

Usage Examples

.i mi jo'u la .clsn. cu ciksi tu'a lo cmavo be zo coi
Me and Shoulson are explaining about the cmavo of selma'o COI.
lo za'e tridu cu mixre lo tricu jo'u lo tcidu
A 'treeder' is a mixture of a tree and a reader.


cmavo: ju'e (JOI)

Proposed Definition

Vague connective. Joins two sumti into one sumti. The referent of the resulting sumti is some function of the referents of both sumti. More than two sumti may be joined into one sumti by chaining up additional { ju'e SUMTI }.

See Also

Proposed Keywords

  • vague connective

Usage Examples

mi'a casnu zo jetnu ju'e zo fatci ju'e lo si'o jetnu ku ju'e lo si'o fatci
We are discussing about "truth"/"fact"/truth/fact. (IRC, Eimi, 22 Dec 2008 07:40:19)
.i ji'a co'e lo plise ju'e lo perli ju'e lo drata
Also an apple and a pear. (IRC, xalbo, 5 Oct 2010 12:50:22)



cmavo: fa'u (JOI)

Proposed Definition

Respectively. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly and distributively in correspondence with another term.

See Also

Proposed Keywords

  • respectively

Usage Examples

mi fa'u do klama lo zdani fa'u lo zarci
Me and you go home and to the market, respectively.
li pano fa'u li cinono cu jdima lo nu klama fu lo girzu karce fa'u lo vinji
Ten and three-hundred are the prices of going by bus and by plane, respectively.


cmavo: joi (JOI)

Proposed Definition

Non-distributive group. Joins two sumti into one sumti. The referents of the resulting sumti are the referents of both sumti considered jointly and non-distributively. More than two sumti may be joined into one sumti by chaining up additional { joi SUMTI }.

See Also

  • {gunma}

Proposed Keywords

  • both
  • together with
  • and

Usage Example

mi joi ry. ze'a casnu lo lijda ctuca tadji
Me and R have been discussing religious teaching methods.
la .djan. joi la .pitr. cu re mei
John and Peter are two.
la jegvon cu cevni le xriso joi le xebro joi le muslo
Jehovah is the god of the Christians, the Jews and the Muslims.


cmavo: ce (JOI)

Proposed Definition

Joins two sumti into one sumti. The referent of the resulting sumti is the set whose members are the referents of both sumti considered jointly. More than two sumti may be joined into one sumti by chaining up additional { ce SUMTI }. Thus, {X ce Y ce Z} creates one single set containing X, Y and Z.

See Also

  • {cmima}

Proposed Keywords

  • and (set)

Usage Examples

.abu ce by ce cy vasru .abu ce by
{a, b, c} ⊇ {a, b}


cmavo: ce'o (JOI)

Proposed Definition

Joins two sumti into one sumti. The referent of the resulting sumti is the sequence whose members are the referents of both sumti considered jointly. More than two sumti may be joined into one sumti by chaining up additional { ce'o SUMTI }.

See Also

  • {porsi}

Proposed Keywords

  • and (sequence)

Usage Examples

jukpa ce'o citka lo cersai co'o ru'e
Making and eating breakfast, bye for now.
.abu ce'o by cu mleca cy ce'u dy .ijo ge .abu mleca cy gi by mleca dy
(a,b) ≤ (c,d) if and only if a ≤ c and b ≤ d


cmavo: jo'e (JOI)

Proposed Definition

Union of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the union of the sets referred to by each sumti. More than two sumti may be joined into one sumti by chaining up additional { jo'e SUMTI }.

See Also

Proposed Keywords

  • union

Usage Examples

lo'i brivla cu du lo'i gismu jo'e lo'i fu'ivla jo'e lo'i lujvo to po'o xu toi
The set of brivla is equal to the union of the set of gismu and the set of fu'ivla and the set of lujvo (only?).


cmavo: ku'a (JOI)

Proposed Definition

Intersection of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the intersection of the sets referred to by each sumti. More than two sumti may be joined into one sumti by chaining up additional { ku'a SUMTI }.

See Also

Proposed Keywords

  • Intersection

Usage Examples

xy cmima .abu ku'a by .ijo ge xy cmima .abu gi xy cmima by
x ∈ A ∩ B if and only if x ∈ A and x ∈ B.


cmavo: pi'u (JOI)

Proposed Definition

Cartesian product of sets. Joins two sumti into one sumti. The referent of the resulting sumti is the set which is the Cartesian product of the sets referred to by each sumti.

See Also

Proposed Keywords

  • Cartesian Product
  • Set Product
  • Cross product

Usage Examples

ko cuxna lo sanmi pi'u gi lo ckafi ce lo tcati gi lo grute ce lo nanba
Choose a meal from the Cartesian product of the set {coffee, tea} and the set {fruits, bread}.
For the meal, choose one of coffee or tea, and one of fruits or bread.
le'i bebna ku pi'u le'i mabla sidbo ku cu barda
The cross product of the set of silly things and the set of bad ideas is large.


Formal definitions

X ju'e Y = lo co'e be X bei Y
X jo'u Y = lo suzmei noi ge X .e Y me ke'a gi ro me ke'a cu me X gi'a me Y
X joi Y = lo gunma be X .e Y
X ce Y = lo se cmima be X .e Y .e no drata be X .e Y
X ce'o Y = lo porsi be fi X jo'u Y be'o noi X lidne Y ke'a
X jo'e Y = lo selcmi noi ro cmima be ke'a cu cmima X .a Y
X ku'a Y = lo selcmi noi ro cmima be ke'a cu cmima X .e Y
X pi'u Y = lo selcmipi'i be X bei Y
sumti1 fa'u sumti2 sumti3 fa'u sumti4 selbri == sumti1 sumti3 selbri .i sumti2 sumti4 selbri

Notes

  1. The definitions given correspond to their use as sumti connectives. Other uses (when they make sense) have yet to be added.

Impact