Difference between revisions of "All about poi and noi"

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'''DO NOT READ YET'''
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''———Written by selpahi———''
  
This page sets out to explain all you need to now about the relative clause markers '''poi''' and '''noi''', how they differ with regards to description sumti, both unquantified and in the presence of quantifiers.
+
{{personal}}
  
The article deliberately ignores '''pe''', '''ne''', '''po'u''' and '''no'u''', because those are nothing more than shortcuts of '''poi''' and '''noi''' combined with specific predicates. Everything that applies to '''poi''' and '''noi''' directly applies to those cmavo, too. No separate explanations are required.
+
<span style="font-size: 300%">'''DO NOT READ YET'''</span>
 +
 
 +
This page sets out to explain all you need to now about the relative clause markers '''poi''' and '''noi'''.
 +
 
 +
It does not contain separate explanations for '''pe''', '''ne''', '''po'u''' and '''no'u''', because those are nothing more than shortcuts of '''poi''' and '''noi''' combined with specific predicates. Everything that applies to '''poi''' and '''noi''' directly applies to those cmavo, too. No separate explanations are required. For a conversion table see the bottom of this page.
  
 
The examples on this page will consist of a Lojban phrase or expression, a rendering in logic notation, and an English translation.
 
The examples on this page will consist of a Lojban phrase or expression, a rendering in logic notation, and an English translation.
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| <math>\forall</math> || universal quantifier
 
| <math>\forall</math> || universal quantifier
 
|-
 
|-
| || logical and
+
| <math>\land</math> || logical and
 +
|-
 +
| <math>\neg</math> || logical negation
 +
|-
 +
| <math>=</math> || sameness, the two operands have the same referents.
 
|-
 
|-
| <math>=<</math> || is-among, Lojban '''me'''
+
| <math>\subseteq</math> || is-among, Lojban '''me'''
 
|-
 
|-
| Q || any (outer) quantifier
+
| <math>\square</math> || any (outer) quantifier
 
|-
 
|-
| x, y, z || singular variables
+
| <math>x, y, z</math> || singular variables
 
|-
 
|-
| xx, yy, zz || plural variables
+
| <math>xx, yy, zz</math> || plural variables
 
|-
 
|-
| c, c<sub>0</sub>, c<sub>1</sub>, ...  || plural constants
+
| <math>c, c_0, c_1\dots</math> || plural constants
 
|-
 
|-
| [] || surrounds prenex
+
| <math>[\cdots]\colon </math> || surrounds prenex
 
|-
 
|-
| : || corresponds to Lojban '''poi'''
+
| <math>\colon</math> || corresponds to Lojban '''poi'''
 
|-
 
|-
| ; || separates sentences, like Lojban '''.i'''
+
| <math>;</math> || separates sentences, like Lojban '''.i'''
 
|}
 
|}
  
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'''poi''' and '''noi''' introduce relative clauses, restrictive and non-restrictive respectively. They help us narrow down referent sets or allow us to provide additional information about a given sumti. For both '''poi''' and '''noi''', their syntactic position and environment make a big difference as to what exactly they achieve in a given sentence. We will look at each and every possible case below.
 
'''poi''' and '''noi''' introduce relative clauses, restrictive and non-restrictive respectively. They help us narrow down referent sets or allow us to provide additional information about a given sumti. For both '''poi''' and '''noi''', their syntactic position and environment make a big difference as to what exactly they achieve in a given sentence. We will look at each and every possible case below.
  
=PA da NOI=
+
==A general note about inner quantifiers==
 +
 
 +
It should be noted that so-called inner quantifiers (the ones between gadri and selbri) aren't true logical quantifiers in that they don't count true bridi, but merely enumerate the number of referents of a sumti. The presence or absence of an inner quantifier has no effect on the behaviour of relative clauses, be it outer or inner relative clauses. What a relative clause means is solely dependent on whether it is a restrictive ('''poi''') or non-restrictive ('''noi''') one, and whether it is an inner ('''lo broda NOI''') or outer ('''lo broda ku NOI''') relative clause.
 +
 
 +
=PA da poi=
 +
 
 +
[...]
 +
 
 +
What does a quantifier do? A quantifier counts how many times or for how many things a bridi is true, or, put another way, a quantifier counts true bridi.
 +
 
 +
[...]
  
==PA da poi==
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domain
  
==PA da noi==
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anything -> anybody
  
=NOI and unquantified sumti=
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examples
  
With plain sumti, a relative clause can only be placed after the sumti (e.g. '''mi noi tatpi''').
 
  
With selbri based descriptions (e.g. '''lo plise'''), there are three different places a relative clause (abbreviated <rel>) can go:
+
A useful thing to know is that a sentence of the form '''su'o da poi broda cu brode''' is truth-functionally equivalent to '''su'o da ge broda gi brode''':
  
{{mu|lo <rel> broda <rel> ku <rel>}}
+
{{mu|su'o da poi ke'a broda cu brode}}
 +
{{lm||equals}}
 +
{{mu|su'o da ge broda gi brode}}
  
By definition, a relative clause that appears between gadri and selbri is equivalent to one that appears after the '''ku''':
+
For example:
  
{{mu|lo <rel> broda}}
+
{{lm|su'o da poi ke'a cribe cu blabi |<math>[\exists x\colon \text{cribe}(x)]\colon \text{blabi}(x)</math> |"Some bears are white."}}
  
is equivalent to:
+
has the same meaning as:
  
{{mu|lo broda ku <rel>}}
+
{{lm|su'o da ge cribe gi blabi |<math>[\exists x]\colon  \text{cribe}(x) \land \text{blabi}(x)</math>|"There exists some X such that X is both a bear and white."}}  
  
Because they are equivalent we will only analyse the case where the relative clause follows '''ku''' to avoid duplication.
+
For '''ro da poi broda cu brode''' the following equivalence holds instead:
  
If the relative clause is placed between selbri and '''ku''' then the meaning changes compared to the other two cases above.
+
{{lm|ro da poi ke'a broda cu brode}}
 +
{{lm||equals}}
 +
{{lm|ro da zo'u ga nai da broda gi da brode}}
  
==<sumti> NOI==
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For example:
  
==lo broda NOI==
+
{{lm|Lojban|<math>logic</math>|"English."}}
  
=something something=
+
which means the same as:
  
There are only two rules to learn, two rules, which explain every possible combination of quantifiers and relative clauses.
+
{{lm|Lojban|<math>logic</math>|"English."}}
  
An inner quantifier isn't a true logical quantifier in that it doesn't count true bridi, but merely enumerates the number of referents of a sumti.
+
==PA <selbri>==
  
An outer quantifier counts how many times or for how many things a bridi is true.
+
By definition, '''PA da poi ke'a broda''' can be abbreviated '''PA broda'''. This is a handy shortcut that saves space, variables, and terminators. Apart from the different grammar, '''PA broda''' behaves identical to '''PA da poi ke'a broda''' in all contexts.
  
{{lm|Q da broda|<math>[Qx] \:  broda(x)</math>}}
+
==PA <sumti>==
  
{{mu|Q <sumti> cu broda}}
+
'''poi''' also appears "invisibly" any time a sumti carries an outer quantifier.
  
{{mu|Q da poi ke'a me <sumti> cu broda}}
+
A quantifier <math>\square</math> counts for how many things that are among the referents of <sumti> the bridi is true, or in other words, it tells you that if you were to substitute each member for <sumti>, then the bridi would be true exactly <math>\square</math> times.
  
The quantifier Q counts for how many things that are among the referents of <sumti> the bridi is true, or in other words,
+
This is the formula that is evoked any time an outer quantifier occurs in a bridi:
  
it tells you that if you were to substitute each member for , then the bridi would be true exactly Q times.
+
{{lm|Q da poi ke'a me <math>c</math> cu broda|<math>[\square x \colon x \subseteq c ]\colon  \text{broda}(x)</math>}}
  
Since {da} is a singular variable, it always stands in for ...
+
[...]
  
This is the formula that is evoked any time an outer quantifier occurs in a bridi.
+
For example:
  
{{lm|Q da poi ke'a me <sumti> cu broda|<math>[Qx : x =< c_s ] \:  broda(x)</math>}}
+
{{lm|Lojban|<math>logic</math>|"English"}}
  
 
[...]
 
[...]
  
{{lm|<sumti> poi ke'a brode cu broda|<math>c_0 =< c_{sumti} \land brode(c_0); \:  broda(c_0)</math>}}
+
{{lm|Lojban|<math>logic</math>|"English"}}
  
'''<sumti> poi ke'a brode''' creates a new sumti whose referents are those that are both among <sumti> and satisfy '''brode'''. It is important to note that ''all'' referents that are among <sumti> and satisfy '''brode''' are among the referents of the resulting expression, not just ''some'' of the referents. This is called maximality.
+
We will need this expansion later when we look at '''PA lo <selbri>''' and its variations.
  
Looking at the logic notation, we can see that the constant c is only stated to be among c1 and to brode, but not that all referents among c1 that brode are among c0, even though that's what the '''poi''' version implies. The following always holds with outer '''poi''':
+
=PA da noi=
  
<math>[Axx] \:  xx =< c_{sumti} \land brode(xx) \to xx =< c_0</math>
+
[...]
  
So the full sentence would actually be:
+
{{lm|Q da broda|<math>[\square x]\colon  \text{broda}(x)</math>}}
  
<math>c_0 =< c_{sumti} \land brode(c_0) \land ([Axx] \:  xx =< c \land brode(xx) \to xx =< c_1); \:  broda(c_0)</math>
+
{{mu|Q <sumti> cu broda}}
  
However, since this takes up so much space, we will omit the part in the middle with the understanding that maximality is implied in all examples involving outer '''poi'''. This is to keep things easier to read.
+
{{mu|Q da poi ke'a me <sumti> cu broda}}
  
{{lm|<sumti> noi ke'a brode cu broda|<math>brode(c); \:  broda(c)</math>}}
 
  
 
[...]
 
[...]
  
{{lm|Q da poi ke'a brode cu broda|<math>[Qx : brode(x)] \: broda(x)</math>}}
+
{{lm|Q da poi ke'a brode cu broda|<math>[\square x \colon \text{brode}(x)]\colon \text{broda}(x)</math>}}
  
 
[...]
 
[...]
  
{{lm|Q da noi ke'a brode cu broda|<math>[Qx] \: broda(x); \:  [Ay : brode(y)] \: broda(y)</math>}}
+
{{lm|Q da noi ke'a brode cu broda|<math>[\square x]\colon \text{broda}(x); [\forall y \colon \text{brode}(y)]\colon \text{broda}(y)</math>}}
  
Whence the universal quantifier? In simple terms, we know that '''noi''' is non-restrictive, which means that its presence must not have any impact on the number of true bridi that the quantifier Q counts. The only logical way in which a relative clause could make a statement without restricting (i.e. selecting a sub-set) is if the predicate of the '''noi'''-clause applies to ''every'' member of a given referent-set.
+
Whence the universal quantifier? In simple terms, we know that '''noi''' is non-restrictive, which means that its presence must not have any impact on the number of true bridi that the quantifier <math>\square</math> counts. The only logical way in which a relative clause could make a statement without restricting (i.e. selecting a sub-set) is if the predicate of the '''noi'''-clause applies to ''every'' member of a given referent-set.
  
 
Prefixing a '''na ku''' to a bridi is always a good way to gain insights about the scope interactions within the bridi. How does such a negation differ between a '''poi''' sentence and a '''noi''' sentence?
 
Prefixing a '''na ku''' to a bridi is always a good way to gain insights about the scope interactions within the bridi. How does such a negation differ between a '''poi''' sentence and a '''noi''' sentence?
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na ku su'o da poi ke'a brode cu broda
 
na ku su'o da poi ke'a brode cu broda
  
<math>![Ex : brode(x)] \: broda(x)</math>
+
<math>\neg [\exists x \colon \text{brode}(x)]\colon \text{broda}(x)</math>
  
<math>[Ax : brode(x)] \: !broda(x)</math>
+
<math>[\forall x \colon \text{brode}(x)]\colon \neg \text{broda}(x)</math>
  
{{mu|na ku su'o da noi ke'a brode cu broda|<math>![Ex] \: broda(x); \:  [Ay : brode(y)] \: broda(y)</math>}}
+
{{mu|na ku su'o da noi ke'a brode cu broda|<math>\neg [\exists x]\colon \text{broda}(x); [\forall y \colon \text{brode}(y)]\colon \text{broda}(y)</math>}}
  
 
In the '''noi''' version, we know that nothing '''broda''', but all things still '''brode''', because '''noi''' makes a separate claim.
 
In the '''noi''' version, we know that nothing '''broda''', but all things still '''brode''', because '''noi''' makes a separate claim.
  
In the '''poi''' version, we know have a much weaker claim, namely that nothing satisfies both '''brode''' and '''broda''' together (broda(x) \land brode(x)), while nothing is said about how many things satisfy '''broda''', and how many satisfy '''brode'''.
+
In the '''poi''' version, we know have a much weaker claim, namely that nothing satisfies both '''brode''' and '''broda''' together (<math>\text{broda}(x) \land \text{brode}(x)</math>), while nothing is said about how many things satisfy '''broda''', and how many satisfy '''brode'''.
 +
 
 +
=<sumti> NOI=
 +
 
 +
==<sumti> noi==
 +
 
 +
Let's begin this section with the simplest case first, '''<sumti> noi'''. This is '''noi''' in its most basic habitat. '''noi''' makes an incidental claim about the head noun which is separate from the main bridi. The general syntax of '''<sumti> noi''' is this:
 +
 
 +
{{lm|<math>c</math> noi ke'a brode cu broda|<math>\text{brode}(c); \text{broda}(c)</math>}}
 +
 
 +
Logically speaking this is the simplest possible use of a relative clause; two simple claims, no quantification. For example:
 +
 
 +
{{lm|mi pilno ti noi ke'a plixau|<math>c = \text{ti}; \text{pilno}(\text{mi}, c); \text{plixau}(c)</math>|"I'm using this, which is useful." / "I'm using this. It's useful."}}
  
'''lo PA broda ku''' is a case of <sumti>, and we already know how <sumti> interacts with quantifiers and relative clauses. There isn't anything new to understand here, but we'll look at an example regardless:
+
What does it mean for the '''noi''' clause to constitute a separate claim? It means that any operators that operate on the main bridi will not affect the content of the '''noi''' clause. For example:
  
{{lm|lo mu plise ku poi xunre cu kukte|<math>plise(c_p) \land mumei(c_p); \: c =< c_p \land xunre(c); \:  kukte(c)</math>}}
+
{{lm|xu do noi ke'a certu ba sidju mi|<math>?\big[\text{sidju}(\text{do}, \text{mi}); \: \text{certu}(\text{do})\big]</math>|"Will you, who are an expert, help me?"}}
  
Quite a different case is '''lo broda poi brode''', where the relative clause is placed between selbri and '''ku'''. Here, '''poi''' acts even before '''lo''' to define the initial predicate of which '''lo''' then extracts the x1.
+
The question word '''xu''' only affects the main bridi, keeping the '''noi''' clause an assertion.
  
{{mu|lo [broda poi brode]}}
+
Similarly so for negation:
  
A '''poi''' in this position is exactly equivalent to '''je poi'i''':
+
{{lm|na ku mi noi prami do cu tolstace|<math>\neg \text{tolstace}(\text{mi}); \text{prami}(\text{mi}, \text{do})</math>|"It's not the case that I, who love you, am dishonest." (i.e., "I love you, and I'm not dishonest."}}
 +
 
 +
While it's possible to translate '''mi noi prami do cu tolstace''' into English as ''"I love you and am being dishonest"'', this is not recommended, because it could suggest that '''noi''' can be translated into '''gi'e''', which it cannot, as becomes apparent when the '''na ku''' is added back in:
 +
 
 +
{{lm|na ku mi prami do gi'e tolstace|<math>\neg ( \text{prami}(\text{mi}, \text{do}) \land \text{tolstace}(\text{mi}))</math>|"It's not the case that I both love you and am being dishonest." (i.e., at least one of those two is false)}}
 +
 
 +
Therefore it's best to always consider the '''noi''' clause as entirely independent from the main claim, lest one could make wrong assumptions.
 +
 
 +
==<sumti> poi==
 +
 
 +
The previous section that '''<sumti> noi''' is very straightforward. It has an obvious meaning and its logic is easy to grasp. '''<sumti> poi''' on the other hand might be less obvious. In the section about '''da poi''' we saw '''poi''' restricting the domain of a quantifier. But here we have no quantifier, so what is the '''poi''', the ''restrictive'' relative clause marker, to restrict in '''<sumti> poi'''?
 +
 
 +
The general syntax of '''<sumti> poi''' is this:
 +
 
 +
{{lm|<math>c</math> poi ke'a brode cu broda|<math>c^\prime \subseteq c \land \text{brode}(c^\prime); \text{broda}(c^\prime)</math>}}
 +
 
 +
What does this mean? It means that '''<sumti> poi ke'a brode''' creates a new sumti whose referents are those that are both among <sumti> and satisfy '''brode'''. Since there is no quantifier whose domain could be restricted, the '''poi''' has to perform a restriction directly on the sumti. It does this by selecting referents from among the sumti which satisfy a certain predicate, namely the predicate inside the relative clause.
 +
 
 +
It is important to note that precisely ''all'' referents that are among <sumti> and satisfy '''brode''' are among the referents of the resulting expression, not just ''some'' of the referents. This is called maximality.
  
{{mu|lo broda je poi'i ke'a brode}}
+
Looking at the logic notation, we can see that the constant <math>c</math> is only stated to be among <math>c1</math> and to '''brode''', but not that all referents among <math>c1</math> that brode are among <math>c0</math>, even though that's what the '''poi''' version implies. The following always holds with outer '''poi''':
  
{{mu|lo poi'i ke'a broda gi'e brode}}
+
<math>[\forall xx]\colon  xx \subseteq c_{\text{sumti}} \land \text{brode}(xx) \implies xx \subseteq c_0</math>
  
Since the inner '''poi''' merely defines the initial referents of the sumti, it has no bearing on outer quantifiers.
+
So the full sentence would actually be:
  
'''lo broda poi brode ku''' is really just another way of writing '''lo <selbri> ku'''.
+
<math>c_0 \subseteq c_{\text{sumti}} \land \text{brode}(c_0) \land ([\forall xx]\colon  xx \subseteq c \land \text{brode}(xx) \implies xx \subseteq c_1); \text{broda}(c_0)</math>
  
lo mu broda poi brode = lo mu brodi
+
However, since this takes up so much space, we will omit the part in the middle with the understanding that maximality is implied in all examples involving outer '''poi'''. This is to keep things easier to read.
  
Five [brodas that brode]
+
Let's look at some examples:
  
{{mu|mi lebna re lo mu plise poi xunre}}
+
{{lm|Lojban|<math>logic</math>|"English."}}
{{lm|re da poi ke'a me lo mu plise poi xunre zo'u mi da lebna|<math>plise(c) \land xunre(c) \land mumei(c); \:  [2x : x =< c] \:  lebna(mi, x)</math>|"I take two of the five red apples."}}
 
  
What happens, when '''poi''' is outside the '''ku'''? Then we get a case we've already covered: ''<sumti>'' '''poi broda'''
+
[...]
  
'''<sumti> poi broda''' is the same as '''lo me <sumti> je broda''', which is the same as '''lo poi'i ke'a me <sumti> gi'e broda'''.
+
{{lm|Lojban|<math>logic</math>|"English."}}
  
We shall now examine the most complicated case, an outer quantifier paired with an outer '''poi''', and then '''noi'''.
+
[...]
  
{{mu|re lo mu plise ku poi xunre cu kukte}}
+
===<sumti> poi with apparently singular <sumti>===
  
Interpretation 1:
+
Certain kinds of sumti tend to be interpreted as singular, like '''mi''' (presupposing a single speaker here), or perhaps a sumti formed with '''zo'''. What effect does using '''poi''' on a sumti like this have, and what does this tell us about '''poi'''?
{{lm|re da poi ke'a me lo mu plise gi'e xunre cu kukte|<math>plise(c) \land mumei(c); \: [2x : x =< c \land xunre(c)] \: kukte(c)</math>|"Two things that are among the five apples and are red are delicious."}}
 
  
Interpretation 2:
+
[...]
{{lm|re lo poi'i ke'a me lo mu plise gi'e xunre cu kukte|<math>plise(c_{plise}) \land mumei(c_{plise}); \: c =< c_{plise} \land xunre(c); \: [2x : x =< c] \: kukte(x)</math>|"Two things that are among those things which are among the five apples and red are delicious."}}
 
  
With this example, the two interpretations give the same result, the same number of delicious apples. However, the next example shows the inadequacy of interpretation 1:
+
=Selbri-based descriptions=
  
{{mu|lo pulji cu arrest reno lo panono demonstrators ku poi sruri lo dinju}}
+
==Relative clause placements==
  
(Note by the way, that the same sentence with inner '''poi''' would translate to English as ''"The police arrested 20 of the 100 building-surrounding demonstrators"'', i.e., all 100 both demonstrated and surrounded the building)
+
A selbri-based description is a sumti made from a gadri plus a selbri, e.g. '''lo plise'''. With selbri-based descriptions there are three different places a relative clause (abbreviated <rel>) can go:
  
Let us again examine the two possible interpretations:
+
{{mu|lo <rel> broda <rel> ku <rel>}}
  
Interpretation 1:
+
By definition, a relative clause that appears between gadri and selbri is equivalent to one that appears after the '''ku''':
  
{{lm|lo pulji cu arrest reno da poi ke'a me lo panono demonstrators gi'e sruri lo dinju|<math>pulji(c_{pulji}); \: demonstrate(c_{demonstrators}) \land panonomei(c_{demonstrator}); \: dinju(c_{dinju}); \: [20x : x =< c_{demonstrators} \land sruri(x,c_{dinju}] \: arrest(c_{pulji}, x)</math>|"The police arrested 20 things that were among the one hundred demonstrators and that surrounded the building."}}
+
{{mu|lo <rel> broda}}
  
Interpretation 2:
+
is equivalent to:
  
{{lm|lo pulji cu arrest reno lo poi'i ke'a me lo panono demonstrators gi'e sruri lo dinju|<math>logic</math>|"The police arrested 20 of those among the 100 demonstrators that surrounded the building"}}
+
{{mu|lo broda ku <rel>}}
  
(100 people were demonstrating, some of them surrounded the building, and 20 of those got arrested)
+
Because they are equivalent we will only analyse the case where the relative clause follows '''ku''' to avoid duplication.
  
Sentence 1 actually means that the police didn't arrest anyone!
+
If the relative clause is placed between selbri and '''ku''' then the meaning changes compared to the other two cases above.
  
This is because interpretation 1 does not account for non-distributive plural predication, while interpretation 2 does.
+
Below we will examine the different possibilities, '''lo broda poi''', '''lo broda noi''', '''lo broda ku poi''' and '''lo broda ku noi''' in detail.
  
What if the outer '''poi''' is replaced with outer '''noi'''?
+
==Inner relative clauses - lo <selbri> NOI==
  
{{mu|mi lebna ci lo mu plise ku noi xunre}}
+
===lo <selbri> poi===
  
Interpretation 1:
+
[...]
  
{{lm|mi lebna ci lo mu plise .i ro plise poi mi lebna ke'a cu xunre|<math>plise(c) \land mumei(c); \:  [3x : x =< c] \:  lebna(mi, x); \:  [Ay : plise(y) \land lebna(mi, y)] \:  xunre(y)</math>|"I take three of the five apples. Each apple that I take is red."}}
+
Quite a different case is '''lo broda poi brode''', where the relative clause is placed between selbri and '''ku'''. Here, '''poi''' semantically acts even before '''lo''' to define the initial predicate of which '''lo''' then extracts the x1. The resulting predicate has the same referent set as the conjunction of the initial predicate and the relative clause.
  
(Note that the '''noi''' version differs significantly from a hypothetical '''poi''' version. With '''noi''' we know that exactly three apples are taken. With '''poi''' we know that three red apples are taken, but not whether any non-red apples are taken)
+
{{mu|lo broda poi brode}}
  
Interpretation 2:
+
A '''poi''' in this position is exactly equivalent to '''je poi'i''':
  
{{lm|lo mu plise cu xunre .i mi lebna ci ri|<math>plise(c) \land mumei(c); \:  xunre(c); \:  [3x : x =< c] \:  lebna(mi, x)</math>|"The five apples are red. I take three of them."}}
+
{{mu|lo broda je poi'i ke'a brode}}
  
Again, both interpretations yield the same number of red apples taken by the speaker (three red apples), but they get to that result by different mechanisms. Which one is correct? Interpretation 1 parallels Interpretation 1 of the '''poi''', and interpretation 2 parallels interpretation 2. We saw that interpretation two of '''poi''' was better, does the same apply to '''noi'''?
+
And this is equivalent to:
  
Let's consider '''noi''' in the context of the demonstrators that surrounded the building:
+
{{mu|lo poi'i ke'a broda gi'e brode}}
  
{{lm|lo pulji cu arrest reno lo panono demonstrators ku noi sruri lo dinju|<math></math>|"The police arrested 20 of the 100 demonstrators, who surrounded the building."}}
+
Since the inner '''poi''' merely defines the initial referents of the sumti, it has no bearing on outer quantifiers. '''lo broda poi brode ku''' is really just a specific case of '''lo <selbri> ku'''.
  
(i.e., 100 people were demonstrating, 20 of those surrounded the building, and all those 20 got arrested)
+
For example:
  
Interpretation 1:
+
{{mu|lo plise poi xunre}}
  
{{lm|lo pulji cu arrest reno da poi ke'a menre lo panono demonstrators .i ro demonstrator poi lo pulji cu arrest ke'a cu sruri lo dinju|<math>pulji(c_{pulji}); \: demonstrate(c_{demonstrators}) \land panonomei(c_{demonstrator}); \: [20x : x =< c_{demonstrators}] \: arrest(c_{pulji}, x); \: dinju(c_{dinju}); \: [\forall y : demonstrator(y) \land arrest(c_{pulji}, y)] \: sruri(y, c_{dinju}</math>|"The police arrested 20 of the 100 demonstrators. Each demonstrator that the police arrested was surrounding the building."}}
+
Yields a sumti that refers to red apples. Let's examine the logic in a full sentence:
  
Note that this does not mean that it's necessarily the case that nobody else among the demonstrators surrounded the building. It does however say that each single arrested demonstrator surrounded the building individually, which is not the intended meaning, and likely a very bizarre situation. Maybe that's why the police felt the need to arrest them.
+
{{lm|mi lebna lo mu plise poi xunre|<math>\text{plise}(c) \land \text{xunre}(c) \land \text{mumei}(c); \text{lebna}(\text{mi}, c)</math>|"I take the five red apples."}}
  
Interpretation 2:
+
Now the same example with an additional outer quantifier:
  
{{lm|lo panono demonstrators cu sruri lo dinju .i lo pulji cu arrest reno lo go'i|</math>|"The 100 demonstrators were surrounding the building. The police arrested 20 of them."}}
+
{{mu|mi lebna re lo mu plise poi xunre}}
 +
{{lm|re da poi ke'a me lo mu plise poi xunre zo'u mi da lebna|<math>\text{plise}(c) \land \text{xunre}(c) \land \text{mumei}(c); \:  [2x \colon x \subseteq c]\colon  \:  \text{lebna}(\text{mi}, x)</math>|"I take two of the five red apples."}}
  
This says that in fact all 100 demonstrators were building-surrounders. Thus, any 20 that the police could arrest automatically are building-surrounders also. Additionally, interpretation 2 again does what interpretation 1 does not: account for plural quantification.
+
[...]
  
But what if we do want to say that what interpretation 1 said (minus the distributivity)?. We might not want to claim each demonstrater a building-surrounder. We might want to say that each arrested demonstrator was a building-surrounder, no, that each arrested demonstrator was ''among'' building-surrounders. Well, we can:
+
What happens, when '''poi''' is outside the '''ku'''? Then we get a case we've already covered: '''<sumti> poi broda''' (we recall that '''<sumti> poi broda''' is the same as '''lo me <sumti> je broda''', which is the same as '''lo poi'i ke'a me <sumti> gi'e broda'''). But we will consider this case in more detail later.
  
{{mu|lo pulji cu arrest reno lo panono demonstrators ku poi sruri lo dinju}}
+
Now, what about inner '''noi'''?
  
{{mu|lo pulji cu arrest reno lo poi'i ke'a me lo panono demonstrators gi'e sruri lo dinju}}
+
===lo <selbri> noi===
  
What about inner '''noi'''?
+
[...]
  
 
{{mu|lo broda noi brode}}
 
{{mu|lo broda noi brode}}
Line 244: Line 292:
 
[...]
 
[...]
  
{{lm|lo plise noi xunre cu kukte|<math>plise(c); \:  xunre(c); \:  kukte(c)</math>}}
+
{{lm|lo plise noi xunre cu kukte|<math>\text{plise}(c); \:  \text{xunre}(c); \:  \text{kukte}(c)</math>}}
  
 
At first glance this looks identical to (5.2) ('''lo plise poi xunre cu kukte''')
 
At first glance this looks identical to (5.2) ('''lo plise poi xunre cu kukte''')
  
{{lm|lo plise poi xunre cu kukte|<math>plise(c) \land xunre(c); \:  kukte(c)</math>}}
+
{{lm|lo plise poi xunre cu kukte|<math>\text{plise}(c) \land \text{xunre}(c); \:  \text{kukte}(c)</math>}}
  
 
(not even a negation could cause a difference here, because the sentence contains nothing but constants)
 
(not even a negation could cause a difference here, because the sentence contains nothing but constants)
Line 260: Line 308:
 
The nuance here is more subtle than with quantifiers and applies directly to the universe of discourse. Let's build an analogue between the quantified noi/poi distinction we already understand, and the inner noi/poi distinction to see the parallels:
 
The nuance here is more subtle than with quantifiers and applies directly to the universe of discourse. Let's build an analogue between the quantified noi/poi distinction we already understand, and the inner noi/poi distinction to see the parallels:
  
{{lm|Q da poi ke'a brode cu broda|<math>[Qx : brode(x)] \:  broda(x)</math>}}
+
{{lm|Q da poi ke'a brode cu broda|<math>[\square x \colon \text{brode}(x)]\colon  \:  \text{broda}(x)</math>|"English"}}
  
 
[...]
 
[...]
  
{{lm|Q da noi ke'a brode cu broda|<math>[Qx] \:  broda(x); \:  [Ay : brode(y)] \:  broda(y)</math>}}
+
{{lm|Q da noi ke'a brode cu broda|<math>[\square x]\colon  \:  \text{broda}(x); \:  [\forall y \colon \text{brode}(y)]\colon  \:  \text{broda}(y)</math>|"English"}}
  
 
As covered much earlier, the '''noi''' implies a universal quantifier, because that's the only logical way that a conjunction can have the same referent set as the predicates in isolation. A similar thing could be said about inner '''noi''', let's compare:
 
As covered much earlier, the '''noi''' implies a universal quantifier, because that's the only logical way that a conjunction can have the same referent set as the predicates in isolation. A similar thing could be said about inner '''noi''', let's compare:
Line 270: Line 318:
 
{{mu|lo broda poi brode cu brodi (replace with actual words!!)}}
 
{{mu|lo broda poi brode cu brodi (replace with actual words!!)}}
  
{{mu|lo poi'i ke'a broda gi'e brode cu brodi}}
+
{{mu|lo poi'i ke'a broda gi'e brode cu brodi|"English"}}
  
 
But in keeping with the theme of creating a new predicate, let's introduce a '''me'au''':
 
But in keeping with the theme of creating a new predicate, let's introduce a '''me'au''':
  
{{lm|lo me'au lo ka broda je lo ka brode cu brodi|<math>broda(c) \land brode(c); \:  brodi(c)</math>}}
+
{{lm|lo me'au lo ka broda je lo ka brode cu brodi|<math>\text{broda}(c) \land \text{brode}(c); \:  \text{brodi}(c)</math>|"English"}}
  
 
The sumti is now very clearly one whose referent(s) satisfy the conjunction of two predicates. What about '''noi'''?
 
The sumti is now very clearly one whose referent(s) satisfy the conjunction of two predicates. What about '''noi'''?
Line 280: Line 328:
 
{{mu|lo broda noi brode cu brodi}}
 
{{mu|lo broda noi brode cu brodi}}
  
{{lm|lo me'au lo ka broda cu brodi .i ro me'au lo ka broda cu me'au lo ka brode|<math>ka(c_F, broda); \:  ka(c_G, brode); \:  ckaji(c, c_F) \land ckaji(c, c_G); \:  brodi(c)</math>}}
+
{{lm|lo me'au lo ka broda cu brodi .i ro'oi me'au lo ka broda cu me'au lo ka brode|<math>\text{ka}(c_F, \text{broda}); \:  \text{ka}(c_G, \text{brode}); \:  \text{ckaji}(c, c_F) \land \text{ckaji}(c, c_G); \:  \text{brodi}(c)</math>|"English"}}
  
 
This could be written simpler if Lojban had a non-restrictive version of '''je''' (something I've proposed it should have), but it doesn't.
 
This could be written simpler if Lojban had a non-restrictive version of '''je''' (something I've proposed it should have), but it doesn't.
Line 287: Line 335:
  
 
No such implication occurs in the '''poi''' version.
 
No such implication occurs in the '''poi''' version.
 +
 +
Again: Inner '''poi''' creates a new predicate that has the same referent set as the conjunction of the two conjoined predicates.
 +
 +
Inner '''noi''' does not create a conjunction, but rather comments on the predicate saying that being '''broda''' also means being '''brode''' (in the current universe of discourse).
 +
 +
==Outer relative clauses - lo <selbri> ku NOI==
 +
 +
===lo <selbri> ku poi===
 +
 +
If you have read everything above, then this section contains no truly new information.
 +
 +
'''lo <selbri> ku''' is a case of '''<sumti>''', and we already know how '''<sumti>''' interacts with quantifiers and relative clauses. There isn't anything new to understand here, but we'll look at an example regardless:
 +
 +
{{lm|lo mu plise ku poi xunre cu kukte|<math>\text{plise}(c_p) \land \text{mumei}(c_p); \:  c \subseteq c_p \land \text{xunre}(c); \:  \text{kukte}(c)</math>|"The red ones among the five apples are delicious."}}
 +
 +
[...]
 +
 +
 +
===lo <selbri> ku noi===
 +
 +
Again, '''lo <selbri> ku noi''' is a case of '''<sumti> noi''', which was covered earlier.
 +
 +
{{lm|lo mu plise ku noi xunre cu kukte|<math>\text{plise}(c_p) \land \text{mumei}(c_p); \: \text{kukte}(c_p); \: \text{xunre}(c_p)</math>|"The five apples, which are red, are delicious."}}
 +
 +
[...]
 +
 +
==PA lo <selbri> ku poi==
 +
 +
We shall now examine the most complicated case, an outer quantifier paired with an outer '''poi''', and then '''noi'''.
 +
 +
{{mu|re lo mu plise ku poi xunre cu kukte}}
 +
 +
<u>Interpretation 1:</u>
 +
{{lm|re da poi ke'a me lo mu plise gi'e xunre cu kukte|<math>\text{plise}(c) \land \text{mumei}(c); \: [2x \colon x \subseteq c \land \text{xunre}(c)]\colon  \: \text{kukte}(c)</math>|"Two things that are among the five apples and are red are delicious."}}
 +
 +
<u>Interpretation 2:</u>
 +
{{lm|re lo poi'i ke'a me lo mu plise gi'e xunre cu kukte|<math>\text{plise}(c_{\text{plise}}) \land \text{mumei}(c_{\text{plise}}); \: c \subseteq c_{\text{plise}} \land \text{xunre}(c); \: [2x \colon x \subseteq c]\colon  \: \text{kukte}(x)</math>|"Two things that are among those things which are among the five apples and red are delicious."}}
 +
 +
With this example, the two interpretations give the same result, the same number of delicious apples. However, the next example shows the inadequacy of interpretation 1:
 +
 +
{{mu|lo pulji cu arrest ro lo panono panja'o ku poi sruri lo dinju}}
 +
 +
(Note by the way, that the same sentence with inner '''poi''' would translate to English as ''"The police arrested each of the 100 building-surrounding demonstrators"'', i.e., all 100 both demonstrated and surrounded the building)
 +
 +
Let us again examine the two possible interpretations:
 +
 +
<u>Interpretation 1:</u>
 +
 +
{{lm|lo pulji cu arrest ro da poi ke'a me lo panono panja'o gi'e sruri lo dinju|<math>\text{pulji}(c_{\text{pulji}}); \: \text{panjaho}(c_{\text{panjaho}}) \land \text{panonomei}(c_{\text{panjaho}}); \: \text{dinju}(c_{\text{dinju}}); \: [\forall x \colon x \subseteq c_{\text{panjaho}} \land \text{sruri}(x,c_{\text{dinju}})]\colon  \: \text{arrest}(c_{\text{pulji}}, x)</math>|"The police arrested each thing that was among the one hundred demonstrators and that surrounded the building."}}
 +
 +
<u>Interpretation 2:</u>
 +
 +
{{lm|lo pulji cu arrest ro lo poi'i ke'a me lo panono panja'o gi'e sruri lo dinju|<math>logic</math>|"The police arrested each of those among the 100 demonstrators that surrounded the building."}}
 +
 +
(100 people were demonstrating, some of them surrounded the building, and all of those got arrested)
 +
 +
With interpretation 1 the police didn't actually arrest anyone! (unless we're dealing with relatives of Mister Fantastic or Plastic Man)
 +
 +
This is because interpretation 1 does not account for non-distributive plural predication, while interpretation 2 does.
 +
 +
Therefore, interpretation 2 is the way to go. As a bonus, it also happens to result in fewer rules, which is always good.
 +
 +
==PA lo <selbri> ku noi==
 +
 +
What if the outer '''poi''' in the previous example is replaced with outer '''noi'''?
 +
 +
{{mu|mi lebna ci lo mu plise ku noi xunre}}
 +
 +
<u>Interpretation 1:</u>
 +
 +
{{lm|mi lebna ci lo mu plise .i ro plise poi mi lebna ke'a cu xunre|<math>\text{plise}(c) \land \text{mumei}(c); \:  [3x \colon x \subseteq c]\colon  \:  \text{lebna}(\text{mi}, x); \:  [\forall y \colon \text{plise}(y) \land \text{lebna}(\text{mi}, y)]\colon  \:  \text{xunre}(y)</math>|"I take three of the five apples. Each apple that I take is red."}}
 +
 +
(Note that the '''noi''' version differs significantly from a hypothetical '''poi''' version. With '''noi''' we know that exactly three apples are taken. With '''poi''' we know that three red apples are taken, but not whether any non-red apples are taken)
 +
 +
<u>Interpretation 2:</u>
 +
 +
{{lm|lo mu plise cu xunre .i mi lebna ci ri|<math>\text{plise}(c) \land \text{mumei}(c); \:  \text{xunre}(c); \:  [3x \colon x \subseteq c]\colon  \:  \text{lebna}(\text{mi}, x)</math>|"The five apples are red. I take three of them."}}
 +
 +
Again, both interpretations yield the same number of red apples taken by the speaker (three red apples), but they get to that result by different mechanisms. Which one is correct? Interpretation 1 parallels Interpretation 1 of the '''poi''', and interpretation 2 parallels interpretation 2. We saw that interpretation two of '''poi''' was better, does the same apply to '''noi'''?
 +
 +
Let's consider '''noi''' in the context of the demonstrators that surrounded the building:
 +
 +
{{mu|lo pulji cu arrest reno lo panono panja'o ku noi sruri lo dinju}}
 +
 +
<u>Interpretation 1:</u>
 +
 +
{{lm|lo pulji cu arrest reno da poi ke'a menre lo panono panja'o .i ro panja'o poi lo pulji cu arrest ke'a cu sruri lo dinju|<math>\text{pulji}(c_{\text{pulji}}); \: \text{panjaho}(c_{\text{panjaho}}) \land \text{panonomei}(c_{\text{panjaho}}); \: [20x \colon x \subseteq c_{\text{panjaho}}]\colon  \: \text{arrest}(c_{\text{pulji}}, x); \: \text{dinju}(c_{\text{dinju}}); \: [\forall y \colon \text{panjaho}(y) \land \text{arrest}(c_{\text{pulji}}, y)]\colon  \: \text{sruri}(y, c_{\text{dinju}})</math>|"The police arrested 20 of the 100 demonstrators. Each demonstrator that the police arrested was surrounding the building."}}
 +
 +
Note that this does not mean that it's necessarily the case that nobody else among the demonstrators surrounded the building. It does however say that each single arrested demonstrator surrounded the building individually, which is not the intended meaning, and likely a very bizarre situation. Maybe that's why the police felt the need to arrest them.
 +
 +
<u>Interpretation 2:</u>
 +
 +
{{lm|lo panono panja'o cu sruri lo dinju .i lo pulji cu arrest reno lo go'i|<math>logic</math>|"The 100 demonstrators were surrounding the building. The police arrested 20 of them."}}
 +
 +
This says that in fact all 100 demonstrators were building-surrounders. Thus, any 20 that the police could arrest automatically are building-surrounders also. Additionally, interpretation 2 again does what interpretation 1 does not: account for plural quantification.
 +
 +
But what if we do want to say that what interpretation 1 said (minus the distributivity)?. We might not want to claim each demonstrater a building-surrounder. We might want to say that each arrested demonstrator was a building-surrounder, no, that each arrested demonstrator was ''among'' building-surrounders. Well, we can:
 +
 +
{{mu|lo pulji cu arrest ro reno lo panono panja'o ku poi sruri lo dinju}}
 +
 +
{{lm|lo pulji cu arrest ro reno lo poi'i ke'a me lo panono panja'o gi'e sruri lo dinju|<math>logic</math>|"The police arrested all 20 of those that were among the 100 demonstrators and that surrounded the building."}}
 +
 +
lo==Relative clauses and la==
 +
 +
la broda NOI
 +
 +
la NOI broda ku'o broda
 +
 +
When to put '''la''' first, and when to put it last?
 +
 +
[...]
 +
 +
{{mu|Lojban|''"English"''}}
 +
 +
[...]
 +
 +
==lo mi <selbri>==
 +
 +
==la and relative clauses==
 +
 +
"President Obama", "Teris the tiger".
 +
 +
[...]
 +
 +
la broda poi
 +
la broda ku poi
 +
 +
la broda noi
 +
la broda ku noi
 +
 +
po'u la broda
 +
 +
[...]
 +
 +
=ma NOI=
 +
 +
First, let's recap how the question word '''ma''' (as well as all the other question words) behave.
 +
ma always has top-scope, no matter how deeply nested it appears in a sentence. (1) and (2) are equivalent:
 +
(1) do djica lo nu mi zukte ma
 +
    "You want me to do what?"
 +
    "What do you want me to do?"
 +
(2) ma poi'i do djica lo nu mi zukte ke'a
 +
    "What is such that you want me to do it?"
 +
    "What is it you want me to do?"
 +
However, if we wish to restrict the referent pool of the question word, the familiar method of using poi (as in (3)) may not be semantically accurate -- the desired expansion of (3) is (4), but the actual meaning is (5). The difference might be subtle and difficult to spot, but it's there, and it means that we should find a new way to say "which/what".
 +
  (3) do pu kanpe lo nu mi cuxna ma poi taxfu
 +
(4) ma taxfu gi'e poi'i do pu kanpe lo nu mi cuxna ke'a
 +
(5) ma poi'i do pu kanpe lo nu mi cuxna ke'a poi taxfu
 +
      ma poi'i do pu kanpe lo nu mi cuxna lo me ke'a je taxfu
 +
One option might be to use noi instead of poi (as in (6)), another would be to use mo (as in (7)).
 +
(6) do pu kanpe lo nu mi cuxna ma noi taxfu
 +
(7) do pu kanpe lo nu mi cuxna lo mo taxfu
 +
      "What kind of clothes did you expect me to choose?"
 +
      "[The] what-clothes did you expect me to choose?"
 +
Both methods leave something to be desired. Even if noi has the right semantics, it still requires a terminator and a ke'a, while using mo can be vague (since it's a tanru) and it can be awkward to use.
 +
 +
Therefore, it might be a good idea to create a new gadri X (in selma'o LO) that has the semantics of (4) but keeps the wh in-situ capability of (3). In other words, '''ko'a broda X brode''' would be defined as '''ma brode gi'e poi'i ko'a broda ke'a'''.
 +
 +
It remains to be decided how that new gadri should be spelled.
 +
 +
=Summary=
 +
 +
[...]
 +
 +
There are only two rules to learn, two rules, which explain every possible combination of quantifiers and relative clauses.
 +
 +
[...]
  
 
With this, we have covered every possible case of relative clauses.
 
With this, we have covered every possible case of relative clauses.
Line 294: Line 509:
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
| su'o da poi ke'a brode cu broda || su'o da ge brode gi broda
+
| '''su'o da poi ke'a brode cu broda''' || '''su'o da ge brode gi broda'''
 +
|-
 +
| '''ro da poi ke'a brode cu broda''' || '''ro da ga nai brode cu broda'''
 +
|-
 +
| '''PA <selbri>''' || '''PA da poi ke'a <selbri>'''
 +
|-
 +
| '''PA <sumti>''' || '''PA da poi ke'a me <sumti>'''
 +
|-
 +
| '''PA da noi ke'a broda cu brode''' || '''PA da broda .i ro broda cu brode'''
 +
|-
 +
| '''<sumti> noi ke'a broda cu brode''' || '''<sumti> brode .i <sumti> broda'''
 
|-
 
|-
| ro da poi ke'a brode cu broda || ro da ga nai brode cu broda
+
| '''<sumti> poi ke'a broda''' || '''lo me <sumti> je poi'i ke'a broda <br> lo poi'i ke'a me <sumti> gi'e broda'''
 
|-
 
|-
| <sumti> poi ke'a broda || lo me <sumti> je broda <br> lo poi'i ke'a me <sumti> gi'e broda
+
| '''lo broda poi brode''' || '''lo broda je poi'i ke'a brode''' <br> '''lo poi'i ke'a broda gi'e brode'''
 
|-
 
|-
| ||
+
| '''lo broda noi brode''' || '''lo broda (to ro'oi broda cu brode toi)'''
 +
|-
 +
| '''lo broda ku poi brode''' || '''lo poi'i ke'a me lo broda gi'e brode'''
 +
|-
 +
| '''lo broda ku noi brode''' || '''lo broda ku (to ri brode toi)'''
 +
|-
 +
| '''lo NOI ke'a brode ku'o broda''' || '''lo broda ku NOI brode'''
 +
|}
 +
 
 +
==Conversion to and from relative phrases==
 +
 
 +
{| class="wikitable"
 
|-
 
|-
| ||
+
| '''pe <sumti>''' || '''poi ke'a co'e <sumti>'''
 
|-
 
|-
| ||
+
| '''ne <sumti>''' || '''noi ke'a co'e <sumti>'''
 
|-
 
|-
| ||
+
| '''po'u <sumti>''' || '''poi ke'a du <sumti>'''
 
|-
 
|-
| ||
+
| '''no'u <sumti>''' || '''noi ke'a du <sumti>'''
 
|-
 
|-
| ||
+
| '''goi <sumti>''' || '''noi ca'e ke'a du <sumti>'''
 
|}
 
|}

Latest revision as of 20:02, 10 January 2019

———Written by selpahi———

DO NOT READ YET

This page sets out to explain all you need to now about the relative clause markers poi and noi.

It does not contain separate explanations for pe, ne, po'u and no'u, because those are nothing more than shortcuts of poi and noi combined with specific predicates. Everything that applies to poi and noi directly applies to those cmavo, too. No separate explanations are required. For a conversion table see the bottom of this page.

The examples on this page will consist of a Lojban phrase or expression, a rendering in logic notation, and an English translation.

Logic symbols used in this article

Symbol Meaning
[math]\exists[/math] existential quantifier
[math]\forall[/math] universal quantifier
[math]\land[/math] logical and
[math]\neg[/math] logical negation
[math]=[/math] sameness, the two operands have the same referents.
[math]\subseteq[/math] is-among, Lojban me
[math]\square[/math] any (outer) quantifier
[math]x, y, z[/math] singular variables
[math]xx, yy, zz[/math] plural variables
[math]c, c_0, c_1\dots[/math] plural constants
[math][\cdots]\colon [/math] surrounds prenex
[math]\colon[/math] corresponds to Lojban poi
[math];[/math] separates sentences, like Lojban .i

poi and noi in general

poi and noi introduce relative clauses, restrictive and non-restrictive respectively. They help us narrow down referent sets or allow us to provide additional information about a given sumti. For both poi and noi, their syntactic position and environment make a big difference as to what exactly they achieve in a given sentence. We will look at each and every possible case below.

A general note about inner quantifiers

It should be noted that so-called inner quantifiers (the ones between gadri and selbri) aren't true logical quantifiers in that they don't count true bridi, but merely enumerate the number of referents of a sumti. The presence or absence of an inner quantifier has no effect on the behaviour of relative clauses, be it outer or inner relative clauses. What a relative clause means is solely dependent on whether it is a restrictive (poi) or non-restrictive (noi) one, and whether it is an inner (lo broda NOI) or outer (lo broda ku NOI) relative clause.

PA da poi

[...]

What does a quantifier do? A quantifier counts how many times or for how many things a bridi is true, or, put another way, a quantifier counts true bridi.

[...]

domain

anything -> anybody

examples


A useful thing to know is that a sentence of the form su'o da poi broda cu brode is truth-functionally equivalent to su'o da ge broda gi brode:

su'o da poi ke'a broda cu brode
equals
su'o da ge broda gi brode

For example:

su'o da poi ke'a cribe cu blabi
[math][\exists x\colon \text{cribe}(x)]\colon \text{blabi}(x)[/math]
"Some bears are white."

has the same meaning as:

su'o da ge cribe gi blabi
[math][\exists x]\colon \text{cribe}(x) \land \text{blabi}(x)[/math]
"There exists some X such that X is both a bear and white."

For ro da poi broda cu brode the following equivalence holds instead:

ro da poi ke'a broda cu brode
equals
ro da zo'u ga nai da broda gi da brode

For example:

Lojban
[math]logic[/math]
"English."

which means the same as:

Lojban
[math]logic[/math]
"English."

PA <selbri>

By definition, PA da poi ke'a broda can be abbreviated PA broda. This is a handy shortcut that saves space, variables, and terminators. Apart from the different grammar, PA broda behaves identical to PA da poi ke'a broda in all contexts.

PA <sumti>

poi also appears "invisibly" any time a sumti carries an outer quantifier.

A quantifier [math]\square[/math] counts for how many things that are among the referents of <sumti> the bridi is true, or in other words, it tells you that if you were to substitute each member for <sumti>, then the bridi would be true exactly [math]\square[/math] times.

This is the formula that is evoked any time an outer quantifier occurs in a bridi:

Q da poi ke'a me [math]c[/math] cu broda
[math][\square x \colon x \subseteq c ]\colon \text{broda}(x)[/math]

[...]

For example:

Lojban
[math]logic[/math]
"English"

[...]

Lojban
[math]logic[/math]
"English"

We will need this expansion later when we look at PA lo <selbri> and its variations.

PA da noi

[...]

Q da broda
[math][\square x]\colon \text{broda}(x)[/math]
Q <sumti> cu broda
Q da poi ke'a me <sumti> cu broda


[...]

Q da poi ke'a brode cu broda
[math][\square x \colon \text{brode}(x)]\colon \text{broda}(x)[/math]

[...]

Q da noi ke'a brode cu broda
[math][\square x]\colon \text{broda}(x); [\forall y \colon \text{brode}(y)]\colon \text{broda}(y)[/math]

Whence the universal quantifier? In simple terms, we know that noi is non-restrictive, which means that its presence must not have any impact on the number of true bridi that the quantifier [math]\square[/math] counts. The only logical way in which a relative clause could make a statement without restricting (i.e. selecting a sub-set) is if the predicate of the noi-clause applies to every member of a given referent-set.

Prefixing a na ku to a bridi is always a good way to gain insights about the scope interactions within the bridi. How does such a negation differ between a poi sentence and a noi sentence?

na ku su'o da poi ke'a brode cu broda

[math]\neg [\exists x \colon \text{brode}(x)]\colon \text{broda}(x)[/math]

[math][\forall x \colon \text{brode}(x)]\colon \neg \text{broda}(x)[/math]

na ku su'o da noi ke'a brode cu broda
[math]\neg [\exists x]\colon \text{broda}(x); [\forall y \colon \text{brode}(y)]\colon \text{broda}(y)[/math]

In the noi version, we know that nothing broda, but all things still brode, because noi makes a separate claim.

In the poi version, we know have a much weaker claim, namely that nothing satisfies both brode and broda together ([math]\text{broda}(x) \land \text{brode}(x)[/math]), while nothing is said about how many things satisfy broda, and how many satisfy brode.

<sumti> NOI

<sumti> noi

Let's begin this section with the simplest case first, <sumti> noi. This is noi in its most basic habitat. noi makes an incidental claim about the head noun which is separate from the main bridi. The general syntax of <sumti> noi is this:

[math]c[/math] noi ke'a brode cu broda
[math]\text{brode}(c); \text{broda}(c)[/math]

Logically speaking this is the simplest possible use of a relative clause; two simple claims, no quantification. For example:

mi pilno ti noi ke'a plixau
[math]c = \text{ti}; \text{pilno}(\text{mi}, c); \text{plixau}(c)[/math]
"I'm using this, which is useful." / "I'm using this. It's useful."

What does it mean for the noi clause to constitute a separate claim? It means that any operators that operate on the main bridi will not affect the content of the noi clause. For example:

xu do noi ke'a certu ba sidju mi
[math]?\big[\text{sidju}(\text{do}, \text{mi}); \: \text{certu}(\text{do})\big][/math]
"Will you, who are an expert, help me?"

The question word xu only affects the main bridi, keeping the noi clause an assertion.

Similarly so for negation:

na ku mi noi prami do cu tolstace
[math]\neg \text{tolstace}(\text{mi}); \text{prami}(\text{mi}, \text{do})[/math]
"It's not the case that I, who love you, am dishonest." (i.e., "I love you, and I'm not dishonest."

While it's possible to translate mi noi prami do cu tolstace into English as "I love you and am being dishonest", this is not recommended, because it could suggest that noi can be translated into gi'e, which it cannot, as becomes apparent when the na ku is added back in:

na ku mi prami do gi'e tolstace
[math]\neg ( \text{prami}(\text{mi}, \text{do}) \land \text{tolstace}(\text{mi}))[/math]
"It's not the case that I both love you and am being dishonest." (i.e., at least one of those two is false)

Therefore it's best to always consider the noi clause as entirely independent from the main claim, lest one could make wrong assumptions.

<sumti> poi

The previous section that <sumti> noi is very straightforward. It has an obvious meaning and its logic is easy to grasp. <sumti> poi on the other hand might be less obvious. In the section about da poi we saw poi restricting the domain of a quantifier. But here we have no quantifier, so what is the poi, the restrictive relative clause marker, to restrict in <sumti> poi?

The general syntax of <sumti> poi is this:

[math]c[/math] poi ke'a brode cu broda
[math]c^\prime \subseteq c \land \text{brode}(c^\prime); \text{broda}(c^\prime)[/math]

What does this mean? It means that <sumti> poi ke'a brode creates a new sumti whose referents are those that are both among <sumti> and satisfy brode. Since there is no quantifier whose domain could be restricted, the poi has to perform a restriction directly on the sumti. It does this by selecting referents from among the sumti which satisfy a certain predicate, namely the predicate inside the relative clause.

It is important to note that precisely all referents that are among <sumti> and satisfy brode are among the referents of the resulting expression, not just some of the referents. This is called maximality.

Looking at the logic notation, we can see that the constant [math]c[/math] is only stated to be among [math]c1[/math] and to brode, but not that all referents among [math]c1[/math] that brode are among [math]c0[/math], even though that's what the poi version implies. The following always holds with outer poi:

[math][\forall xx]\colon xx \subseteq c_{\text{sumti}} \land \text{brode}(xx) \implies xx \subseteq c_0[/math]

So the full sentence would actually be:

[math]c_0 \subseteq c_{\text{sumti}} \land \text{brode}(c_0) \land ([\forall xx]\colon xx \subseteq c \land \text{brode}(xx) \implies xx \subseteq c_1); \text{broda}(c_0)[/math]

However, since this takes up so much space, we will omit the part in the middle with the understanding that maximality is implied in all examples involving outer poi. This is to keep things easier to read.

Let's look at some examples:

Lojban
[math]logic[/math]
"English."

[...]

Lojban
[math]logic[/math]
"English."

[...]

<sumti> poi with apparently singular <sumti>

Certain kinds of sumti tend to be interpreted as singular, like mi (presupposing a single speaker here), or perhaps a sumti formed with zo. What effect does using poi on a sumti like this have, and what does this tell us about poi?

[...]

Selbri-based descriptions

Relative clause placements

A selbri-based description is a sumti made from a gadri plus a selbri, e.g. lo plise. With selbri-based descriptions there are three different places a relative clause (abbreviated <rel>) can go:

lo <rel> broda <rel> ku <rel>

By definition, a relative clause that appears between gadri and selbri is equivalent to one that appears after the ku:

lo <rel> broda

is equivalent to:

lo broda ku <rel>

Because they are equivalent we will only analyse the case where the relative clause follows ku to avoid duplication.

If the relative clause is placed between selbri and ku then the meaning changes compared to the other two cases above.

Below we will examine the different possibilities, lo broda poi, lo broda noi, lo broda ku poi and lo broda ku noi in detail.

Inner relative clauses - lo <selbri> NOI

lo <selbri> poi

[...]

Quite a different case is lo broda poi brode, where the relative clause is placed between selbri and ku. Here, poi semantically acts even before lo to define the initial predicate of which lo then extracts the x1. The resulting predicate has the same referent set as the conjunction of the initial predicate and the relative clause.

lo broda poi brode

A poi in this position is exactly equivalent to je poi'i:

lo broda je poi'i ke'a brode

And this is equivalent to:

lo poi'i ke'a broda gi'e brode

Since the inner poi merely defines the initial referents of the sumti, it has no bearing on outer quantifiers. lo broda poi brode ku is really just a specific case of lo <selbri> ku.

For example:

lo plise poi xunre

Yields a sumti that refers to red apples. Let's examine the logic in a full sentence:

mi lebna lo mu plise poi xunre
[math]\text{plise}(c) \land \text{xunre}(c) \land \text{mumei}(c); \text{lebna}(\text{mi}, c)[/math]
"I take the five red apples."

Now the same example with an additional outer quantifier:

mi lebna re lo mu plise poi xunre
re da poi ke'a me lo mu plise poi xunre zo'u mi da lebna
[math]\text{plise}(c) \land \text{xunre}(c) \land \text{mumei}(c); \: [2x \colon x \subseteq c]\colon \: \text{lebna}(\text{mi}, x)[/math]
"I take two of the five red apples."

[...]

What happens, when poi is outside the ku? Then we get a case we've already covered: <sumti> poi broda (we recall that <sumti> poi broda is the same as lo me <sumti> je broda, which is the same as lo poi'i ke'a me <sumti> gi'e broda). But we will consider this case in more detail later.

Now, what about inner noi?

lo <selbri> noi

[...]

lo broda noi brode
lo poi'i ke'a broda (to ri brode toi)

[...]

lo plise noi xunre cu kukte
[math]\text{plise}(c); \: \text{xunre}(c); \: \text{kukte}(c)[/math]

At first glance this looks identical to (5.2) (lo plise poi xunre cu kukte)

lo plise poi xunre cu kukte
[math]\text{plise}(c) \land \text{xunre}(c); \: \text{kukte}(c)[/math]

(not even a negation could cause a difference here, because the sentence contains nothing but constants)

As we've seen above, an inner poi clause attaches directly to the selbri, in a sense restricting the referent set of the predicate by replacing the single predicate with a conjunction of it and another predicate.

In other words, the poi in lo broda poi brode creates a new predicate [math]H[/math] that has the same referent set as [math]F \land G[/math].

In this sense, poi performs a restrictive roll, even in the absence of any logical quantifiers. noi, however, is the non-restrictive counterpart. It, too, will try to attach directly to the predicate, but without restricting the referent set of the resulting predicate. This means that it does not create a new predicate, or, perhaps more accurately, the referent set of [math]F \land G[/math] in the case of noi is equivalent to that of the lone predicate [math]F[/math].

The nuance here is more subtle than with quantifiers and applies directly to the universe of discourse. Let's build an analogue between the quantified noi/poi distinction we already understand, and the inner noi/poi distinction to see the parallels:

Q da poi ke'a brode cu broda
[math][\square x \colon \text{brode}(x)]\colon \: \text{broda}(x)[/math]
"English"

[...]

Q da noi ke'a brode cu broda
[math][\square x]\colon \: \text{broda}(x); \: [\forall y \colon \text{brode}(y)]\colon \: \text{broda}(y)[/math]
"English"

As covered much earlier, the noi implies a universal quantifier, because that's the only logical way that a conjunction can have the same referent set as the predicates in isolation. A similar thing could be said about inner noi, let's compare:

lo broda poi brode cu brodi (replace with actual words!!)
lo poi'i ke'a broda gi'e brode cu brodi
"English"

But in keeping with the theme of creating a new predicate, let's introduce a me'au:

lo me'au lo ka broda je lo ka brode cu brodi
[math]\text{broda}(c) \land \text{brode}(c); \: \text{brodi}(c)[/math]
"English"

The sumti is now very clearly one whose referent(s) satisfy the conjunction of two predicates. What about noi?

lo broda noi brode cu brodi
lo me'au lo ka broda cu brodi .i ro'oi me'au lo ka broda cu me'au lo ka brode
[math]\text{ka}(c_F, \text{broda}); \: \text{ka}(c_G, \text{brode}); \: \text{ckaji}(c, c_F) \land \text{ckaji}(c, c_G); \: \text{brodi}(c)[/math]
"English"

This could be written simpler if Lojban had a non-restrictive version of je (something I've proposed it should have), but it doesn't.

Thus, we can conclude that the previous example implies a universe of discourse where [math]F[/math] and [math]F \land G[/math] have the same referent set, or put another way, in which for all things, being broda entails being brode.

No such implication occurs in the poi version.

Again: Inner poi creates a new predicate that has the same referent set as the conjunction of the two conjoined predicates.

Inner noi does not create a conjunction, but rather comments on the predicate saying that being broda also means being brode (in the current universe of discourse).

Outer relative clauses - lo <selbri> ku NOI

lo <selbri> ku poi

If you have read everything above, then this section contains no truly new information.

lo <selbri> ku is a case of <sumti>, and we already know how <sumti> interacts with quantifiers and relative clauses. There isn't anything new to understand here, but we'll look at an example regardless:

lo mu plise ku poi xunre cu kukte
[math]\text{plise}(c_p) \land \text{mumei}(c_p); \: c \subseteq c_p \land \text{xunre}(c); \: \text{kukte}(c)[/math]
"The red ones among the five apples are delicious."

[...]


lo <selbri> ku noi

Again, lo <selbri> ku noi is a case of <sumti> noi, which was covered earlier.

lo mu plise ku noi xunre cu kukte
[math]\text{plise}(c_p) \land \text{mumei}(c_p); \: \text{kukte}(c_p); \: \text{xunre}(c_p)[/math]
"The five apples, which are red, are delicious."

[...]

PA lo <selbri> ku poi

We shall now examine the most complicated case, an outer quantifier paired with an outer poi, and then noi.

re lo mu plise ku poi xunre cu kukte

Interpretation 1:

re da poi ke'a me lo mu plise gi'e xunre cu kukte
[math]\text{plise}(c) \land \text{mumei}(c); \: [2x \colon x \subseteq c \land \text{xunre}(c)]\colon \: \text{kukte}(c)[/math]
"Two things that are among the five apples and are red are delicious."

Interpretation 2:

re lo poi'i ke'a me lo mu plise gi'e xunre cu kukte
[math]\text{plise}(c_{\text{plise}}) \land \text{mumei}(c_{\text{plise}}); \: c \subseteq c_{\text{plise}} \land \text{xunre}(c); \: [2x \colon x \subseteq c]\colon \: \text{kukte}(x)[/math]
"Two things that are among those things which are among the five apples and red are delicious."

With this example, the two interpretations give the same result, the same number of delicious apples. However, the next example shows the inadequacy of interpretation 1:

lo pulji cu arrest ro lo panono panja'o ku poi sruri lo dinju

(Note by the way, that the same sentence with inner poi would translate to English as "The police arrested each of the 100 building-surrounding demonstrators", i.e., all 100 both demonstrated and surrounded the building)

Let us again examine the two possible interpretations:

Interpretation 1:

lo pulji cu arrest ro da poi ke'a me lo panono panja'o gi'e sruri lo dinju
[math]\text{pulji}(c_{\text{pulji}}); \: \text{panjaho}(c_{\text{panjaho}}) \land \text{panonomei}(c_{\text{panjaho}}); \: \text{dinju}(c_{\text{dinju}}); \: [\forall x \colon x \subseteq c_{\text{panjaho}} \land \text{sruri}(x,c_{\text{dinju}})]\colon \: \text{arrest}(c_{\text{pulji}}, x)[/math]
"The police arrested each thing that was among the one hundred demonstrators and that surrounded the building."

Interpretation 2:

lo pulji cu arrest ro lo poi'i ke'a me lo panono panja'o gi'e sruri lo dinju
[math]logic[/math]
"The police arrested each of those among the 100 demonstrators that surrounded the building."

(100 people were demonstrating, some of them surrounded the building, and all of those got arrested)

With interpretation 1 the police didn't actually arrest anyone! (unless we're dealing with relatives of Mister Fantastic or Plastic Man)

This is because interpretation 1 does not account for non-distributive plural predication, while interpretation 2 does.

Therefore, interpretation 2 is the way to go. As a bonus, it also happens to result in fewer rules, which is always good.

PA lo <selbri> ku noi

What if the outer poi in the previous example is replaced with outer noi?

mi lebna ci lo mu plise ku noi xunre

Interpretation 1:

mi lebna ci lo mu plise .i ro plise poi mi lebna ke'a cu xunre
[math]\text{plise}(c) \land \text{mumei}(c); \: [3x \colon x \subseteq c]\colon \: \text{lebna}(\text{mi}, x); \: [\forall y \colon \text{plise}(y) \land \text{lebna}(\text{mi}, y)]\colon \: \text{xunre}(y)[/math]
"I take three of the five apples. Each apple that I take is red."

(Note that the noi version differs significantly from a hypothetical poi version. With noi we know that exactly three apples are taken. With poi we know that three red apples are taken, but not whether any non-red apples are taken)

Interpretation 2:

lo mu plise cu xunre .i mi lebna ci ri
[math]\text{plise}(c) \land \text{mumei}(c); \: \text{xunre}(c); \: [3x \colon x \subseteq c]\colon \: \text{lebna}(\text{mi}, x)[/math]
"The five apples are red. I take three of them."

Again, both interpretations yield the same number of red apples taken by the speaker (three red apples), but they get to that result by different mechanisms. Which one is correct? Interpretation 1 parallels Interpretation 1 of the poi, and interpretation 2 parallels interpretation 2. We saw that interpretation two of poi was better, does the same apply to noi?

Let's consider noi in the context of the demonstrators that surrounded the building:

lo pulji cu arrest reno lo panono panja'o ku noi sruri lo dinju

Interpretation 1:

lo pulji cu arrest reno da poi ke'a menre lo panono panja'o .i ro panja'o poi lo pulji cu arrest ke'a cu sruri lo dinju
[math]\text{pulji}(c_{\text{pulji}}); \: \text{panjaho}(c_{\text{panjaho}}) \land \text{panonomei}(c_{\text{panjaho}}); \: [20x \colon x \subseteq c_{\text{panjaho}}]\colon \: \text{arrest}(c_{\text{pulji}}, x); \: \text{dinju}(c_{\text{dinju}}); \: [\forall y \colon \text{panjaho}(y) \land \text{arrest}(c_{\text{pulji}}, y)]\colon \: \text{sruri}(y, c_{\text{dinju}})[/math]
"The police arrested 20 of the 100 demonstrators. Each demonstrator that the police arrested was surrounding the building."

Note that this does not mean that it's necessarily the case that nobody else among the demonstrators surrounded the building. It does however say that each single arrested demonstrator surrounded the building individually, which is not the intended meaning, and likely a very bizarre situation. Maybe that's why the police felt the need to arrest them.

Interpretation 2:

lo panono panja'o cu sruri lo dinju .i lo pulji cu arrest reno lo go'i
[math]logic[/math]
"The 100 demonstrators were surrounding the building. The police arrested 20 of them."

This says that in fact all 100 demonstrators were building-surrounders. Thus, any 20 that the police could arrest automatically are building-surrounders also. Additionally, interpretation 2 again does what interpretation 1 does not: account for plural quantification.

But what if we do want to say that what interpretation 1 said (minus the distributivity)?. We might not want to claim each demonstrater a building-surrounder. We might want to say that each arrested demonstrator was a building-surrounder, no, that each arrested demonstrator was among building-surrounders. Well, we can:

lo pulji cu arrest ro reno lo panono panja'o ku poi sruri lo dinju
lo pulji cu arrest ro reno lo poi'i ke'a me lo panono panja'o gi'e sruri lo dinju
[math]logic[/math]
"The police arrested all 20 of those that were among the 100 demonstrators and that surrounded the building."

lo==Relative clauses and la==

la broda NOI

la NOI broda ku'o broda

When to put la first, and when to put it last?

[...]

Lojban
"English"

[...]

lo mi <selbri>

la and relative clauses

"President Obama", "Teris the tiger".

[...]

la broda poi la broda ku poi

la broda noi la broda ku noi

po'u la broda

[...]

ma NOI

First, let's recap how the question word ma (as well as all the other question words) behave. ma always has top-scope, no matter how deeply nested it appears in a sentence. (1) and (2) are equivalent:

(1) do djica lo nu mi zukte ma
    "You want me to do what?"
    "What do you want me to do?"
(2) ma poi'i do djica lo nu mi zukte ke'a
    "What is such that you want me to do it?"
    "What is it you want me to do?"

However, if we wish to restrict the referent pool of the question word, the familiar method of using poi (as in (3)) may not be semantically accurate -- the desired expansion of (3) is (4), but the actual meaning is (5). The difference might be subtle and difficult to spot, but it's there, and it means that we should find a new way to say "which/what".

 (3) do pu kanpe lo nu mi cuxna ma poi taxfu
(4) ma taxfu gi'e poi'i do pu kanpe lo nu mi cuxna ke'a
(5) ma poi'i do pu kanpe lo nu mi cuxna ke'a poi taxfu
     ma poi'i do pu kanpe lo nu mi cuxna lo me ke'a je taxfu

One option might be to use noi instead of poi (as in (6)), another would be to use mo (as in (7)).

(6) do pu kanpe lo nu mi cuxna ma noi taxfu
(7) do pu kanpe lo nu mi cuxna lo mo taxfu
     "What kind of clothes did you expect me to choose?"
     "[The] what-clothes did you expect me to choose?"

Both methods leave something to be desired. Even if noi has the right semantics, it still requires a terminator and a ke'a, while using mo can be vague (since it's a tanru) and it can be awkward to use.

Therefore, it might be a good idea to create a new gadri X (in selma'o LO) that has the semantics of (4) but keeps the wh in-situ capability of (3). In other words, ko'a broda X brode would be defined as ma brode gi'e poi'i ko'a broda ke'a.

It remains to be decided how that new gadri should be spelled.

Summary

[...]

There are only two rules to learn, two rules, which explain every possible combination of quantifiers and relative clauses.

[...]

With this, we have covered every possible case of relative clauses.

Conversion formulas

su'o da poi ke'a brode cu broda su'o da ge brode gi broda
ro da poi ke'a brode cu broda ro da ga nai brode cu broda
PA <selbri> PA da poi ke'a <selbri>
PA <sumti> PA da poi ke'a me <sumti>
PA da noi ke'a broda cu brode PA da broda .i ro broda cu brode
<sumti> noi ke'a broda cu brode <sumti> brode .i <sumti> broda
<sumti> poi ke'a broda lo me <sumti> je poi'i ke'a broda
lo poi'i ke'a me <sumti> gi'e broda
lo broda poi brode lo broda je poi'i ke'a brode
lo poi'i ke'a broda gi'e brode
lo broda noi brode lo broda (to ro'oi broda cu brode toi)
lo broda ku poi brode lo poi'i ke'a me lo broda gi'e brode
lo broda ku noi brode lo broda ku (to ri brode toi)
lo NOI ke'a brode ku'o broda lo broda ku NOI brode

Conversion to and from relative phrases

pe <sumti> poi ke'a co'e <sumti>
ne <sumti> noi ke'a co'e <sumti>
po'u <sumti> poi ke'a du <sumti>
no'u <sumti> noi ke'a du <sumti>
goi <sumti> noi ca'e ke'a du <sumti>