Difference between revisions of "BPFK Section: Non-logical Connectives"
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({pi'u}: "Cross product" replaced by "Cartesian product" in the main definition. Another example of usage added.) |
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==== Proposed Definition ==== | ==== Proposed Definition ==== | ||
− | + | Cartesian 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. | |
==== See Also ==== | ==== See Also ==== | ||
==== Proposed Keywords ==== | ==== Proposed Keywords ==== | ||
+ | * Cartesian Product | ||
* Set Product | * Set Product | ||
− | * | + | * Cross product |
==== Usage 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}} | {{BPFK Section box close}} |
Revision as of 14:13, 2 April 2016
- This page is imported from version 22 of the page BPFK Section: Non-logical Connectives from the lojban Tiki.
Contents
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 cross 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
- The definitions given correspond to their use as sumti connectives. Other uses (when they make sense) have yet to be added.