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!!Lojban Lessons - Lesson twenty-seven (lojban logic: da, bu'a, zo'u and terms)
- The stated topic of this lesson needs some justification: This lesson is not really about how do to logic in Lojban, since firstly, logic is presumably the same in all languages, and secondly, actually teaching logic would be totally impractical in one single lesson. Rather, this lesson is explains some constructs which resembles those which logicians use. It turns out they have a remarkable wide range of uses in Lojban.
+ The stated topic of this lesson needs some justification: This lesson is not really about how do to logic in Lojban, since firstly, logic is presumably the same in all languages, and secondly, actually teaching logic would be totally impractical in one single lesson. Rather, this lesson explains some constructs which resemble those which logicians use. It turns out they have a remarkable wide range of uses in Lojban.
Getting involved in the more obscure details of these logical constructs can be mind-warpingly difficult, and there will always be some disagreement in the corners of this part of the language.
Learning these logical constructs requires one to learn a bit about constructs which are not logical in nature. Let's begin with ''zo'u''




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!Lojban Wave Lessons Continued (part three):

!!!Made by la klaku with help from various lojbanists. Based on the work of la .kribacr. Spring 2013.



Welcome to the third part of The Wavelessonscontinued. If you want to go back to ((wavelessonscontinued|the first part)) or ((wavelessonscontinuedp2|the second part)), just click on the words representing them in this sentence. This third part is about advanced Lojban. The Lojban in this part is rarely relevant when speaking Lojban in normal contexts, but it pops up quite often when speaking about language and logic. 

These corners of Lojban is for the most part experimental, new or complex, so you should expect a lot of changing definitions, outdated definitions, disagreements and misunderstandings on the part of the author of this text. Sorry about that.



!!Lojban Lessons - Lesson twenty-seven (lojban logic: da, bu'a, zo'u and terms)

The stated topic of this lesson needs some justification: This lesson is not really about how do to logic in Lojban, since firstly, logic is presumably the same in all languages, and secondly, actually teaching logic would be totally impractical in one single lesson. Rather, this lesson explains some constructs which resemble those which logicians use. It turns out they have a remarkable wide range of uses in Lojban.

Getting involved in the more obscure details of these logical constructs can be mind-warpingly difficult, and there will always be some disagreement in the corners of this part of the language.

Learning these logical constructs requires one to learn a bit about constructs which are not logical in nature. Let's begin with ''zo'u''

__''zo'u''__ Separates prenex from bridi

Before any ''zo'u'' is the prenex, after ''zo'u'' is the bridi. Informally, a prenex is a place in front of the bridi, where you put a bunch of terms. A term is an English word given to some kinds of Lojban constructs: Sumti, sumtcita with or without sumti attached, ''na ku'' and an abomination called __termsets__, which I refuse to include in these lessons. The prenex is not part of the bridi, but any terms put inside it gives us information about the bridi. One can, for example, use it to state a topic as shown thus:

''lo pampe'o je nai speni zo'u mi na zanru'' - "Concerning lovers who are not spouses: I do not approve". The benefits of kind of sentence structuring is questionable, but it's always good to have some variation to play with. Furthermore, constructing sentences this way resembles Mandarin (and other languages) closely, meaning it might seem more intuitive for speakers of that language.

__''pampe'o''__ x1 is a lover of x2

__''zanru''__ x1 approves of x2 (plan, event or action)

Of course, the relation between the terms in the prenex and the bridi is vague. One can imagine any sumti in the prenex bearing the same relevance to the bridi as if they were put in the bridi after a ''do'e'' sumtcita, and any sumtcita in the prenex doing pretty much the same as if they were in the bridi. It is quite possible to put terms in prenexes without any clear hints as to how the term may relate to the bridi:

''le vi gerku zo'u mi to'e nelci lo cidjrpitsa'' - "Concerning this dog here: I dislike pizza." It leaves you guessing about the reason for mentioning the dog.

__''cidjrpitsa''__ x1 is pizza with topping/ingredients x2

If the prenex contains ''na ku'', it's pretty straight forward: The entire bridi is negated, just as if the bridi itself began with ''na ku''.

So how long does a prenex last? It lasts until the following bridi is terminated. If that is not desired, there are two ways to make it apply to several bridi: One is to put some kind of connective after the ''.i'' separating the bridi, and another method is to simply include all of the text in ''tu'e'' ... ''tu'u''-brackets. These brackets work pretty much by gluing all the bridi together and makes all sorts of construct apply to several bridi.

Now that we covered ''zo'u'', the first "logical" words we can use it with are these:

__''da''__ logically quantified existential sumka'i 1

__''de''__ logically quantified existential sumka'i 2

__''di''__ logically quantified existential sumka'i 3

These words are all the same, like the mathematical variables x, y and z. Once you have defined them, however, they keep refering to the same thing. These words are defined in the prenex of bridi, meaning that when the prenex stop applying, the definition of these three words are cancelled.

The words ''da'', ''de'' and ''di'' can refer to literally any sumti, which makes them kind of useless unless restricted in some way. The first and foremost way to restrict them is to quantify them: They are not called "logically quantified existential sumka'i" for nothing. They are sumka'i, they are most useful when quantified, and they are existential. What does it mean, being "existential"? It means that if they are used, that implies that they actually refer to something which exists. An example:

The statement ''pa da zo'u da gerku'' has ''pa da'' in the prenex, which means "Concerning one existing thing:", and then ''da'', now defined, is used in the bridi ''da gerku''. Translated to English, this means: "There exists one thing which is a dog". This is obviously false, there are around 400,000,000 of them in the world. If ''da'' and its sisters are not quantified, the number ''su'o'' is the default. Thus ''da zo'u da gerku'' means "There exist at least one thing which is a dog", which is true. Notice here, that any quantification must be more or less exact in order to be true: Of course one dog exists, but in Lojban, ''pa da zo'u da gerku'' means not only that does one dog exists, but also that no more than one does. 

There are a few specific rules to these existential sumka'i:

- If the quantifier ''ro'' is used before ''da'', it instead refers to "all which exists".

- Importantly, the usage of an existential sumka'i only asserts that such a thing exists __in the domain of truth where it's used__. Thus, in the sentence ''so'e verba cu krici lo du'u su'o da crida'', does not state ''da crida'', since its "domain of truth" is only inside the du'u-abstraction. Generally speaking, abstractions contain their own domain of truth, so using ''da'' and friends inside an abstraction is usually safe.

- If the same variable is quantified several times, the first quantification is the one which sticks: Any later quantified instance of that variable can refer only to things which are also being referred to by the first instance of that variable, and any later non-quantified instance of that variable will gain the first quantifier. To use an example: ''ci da zo'u re da barda .ije da pelxu'' means "There exists three things such that two of them are big and all three are yellow". ''re da'', being after ''ci da'', can only refer to two of the already stated three things. When ''da'' appears without a quantifier, ''ci'' is assumed.

- If there are several terms in the prenex, the terms are always read left to right. Sometimes, this matters: ''ro da de zo'u da prami de'' means "Concerning all the things X that exists, concerning at least one thing Y: X loves Y". This is the same as "All things love at least one thing.", where the "thing(s)" can be anything, including the thing itself. Note here that ''de'' can refer to different things for each ''da'' - the thing which is referred to by ''de'' is dependent on the ''da'', since it came before it in the prenex, therefore each thing might love something different. If we switched the places of ''da'' and ''de'' in the prenex, a different result would arise: ''de ro da zo'u da prami de'' = "Concerning at least one thing Y, concerning all X which exists: X loves Y", meaning "There exists at least one thing which everything loves".

Of course, both claims are completely false. There are many things which loves nothing - rocks, or abstract concepts, for example. Likewise, it's impossible to concieve of something which everything loves, since "everything" also encompasses non-sentient things. We need better ways to restrict what these variables can point to. One good way of doing it is to make them the subject of a relative clause:

''ro di poi remna zo'u birka di'' = "Concerning all X that exists, which is human: X has one or more arms." or "All humans have arms", which is true, at least when speaking in a potential, timeless sense.

__''birka''__ x1 is an arm of x2

When restricting claims using this kind of logical "existential" variable, it's very important to remember that unless there is an explicit ''no'' as a quantifier, these kind of statements always imply that there __actually exists__ something which can be referred to by ''da''. Therefore, any kind of non-negated statement where ''da'' points to something which does not exist is false, as in this example: ''ro da poi pavyseljirna zo'u da se jirna'' - "All unicorns have horns". This is wrong because, since ''da'' is existensial, it also means that there must exist at least one unicorn.

Interestingly, when using a relative clause, the variable is being restricted regardless of whether you use ''poi'' or ''noi''. This is because ''re da noi gerku'' still only can refer to two things which are humans. Therefore, ''noi'' makes little sense with ''da''/''de''/''di''. Any clause is always restrictive, unless it's really stupid and obvious like ''de noi gerku cu gerku''.

In fact, you don't really need the prenex to define the variables. You can use them directly as sumti in the bridi, and quantify them there. You only need to quantify them the first time they appear, though. Thus, the sentence about humans having arms could be turned into ''birka ro di poi remna''. The order of the variables still matters though, and so the prenex can be used to avoid having to mess up your bridi to place the variables in the correct order. When having more variables, a prenex is usually a good idea.

The second kind of logical words are basically the same as the three we have already been though, but these are brika'i instead of sumka'i:

__''bu'a''__ logically quantified existential brika'i 1

__''bu'e''__ logically quantified existential brika'i 2

__''bu'i''__ logically quantified existential brika'i 3

These work pretty much the same way as the other three, but there are a few points which are important to mention:

Since only terms can go in the prenex, these brika'i need to have a quantifier in order to make them into sumti. When quantified in the prenex, however, the quantifier works very different from quantifiers with normal selbri: Instead of quantifying the amount of things which fits the x1 of the selbri variable, it directly quantifies the amount of selbri which applies. Again, the default quantifier is ''so'u''. Thus, instead of ''re bu'a zo'u'' meaning "Concerning two things which is in relationship X:", it means "Concerning two relationships X:"

It's probably good to see an example of ''bu'a'' put to practice:

''ro da bu'a la .bab.'' = "Considering all X which exists: X is in at least one relationship with Bob" = "Everything is related to Bob in at least one way.". Notice again the order matters: ''bu'a ro da zo'u da bu'a Bob'' means: "There is at least one relationship such that everything that exists is in that relationship with Bob". The first statement is true - for any one thing, one can indeed make up some selbri which relates any guy called Bob and it. But I'm not sure the latter is true - that one can make a selbri which can relate anything, no matter what it is, and Bob.

Let's have an example which quantifies selbri:

''ci'i bu'e zo'u mi bu'e do'' - "Concerning an infinite amount of relationships: I am in all those relationship with you." or "There exists an infinite amount of relationships between us"

You can't quantify the selbri variables in the bridi itself, though. Then it will act as a sumti: ''mi ci'i bu'a do'' is not a bridi. There are some situation where this will become problematic - lesson twenty-nine will teach how to overcome those problems.



!!Lojban Lessons - Lesson twenty-eight (semantics of simple abstractions)

I feel it is necessary to repeat part of the disclaimer from the beginning of this part of the Wavelessonscontinued: What you find in this lesson and the following is not golden BPFK-definitions, but one interpretation. I have pieced the lessons together from the best and most consistent theories on Lojban, but mind that what is taught in here might not be what all lojbanists agree on.

While you have been taught about abstractions twenty-two lessons ago, there are still many types of abstraction with which you are unfamiliar, and some of the ones you are familiar with have not been properly defined.

The first and most basic abstractor is ''su’u'', which you already know.

You might remember from lesson six that ''su'u'' had a place structure with two sumti places. The second sumti place of ''su'u'' makes the word versatile, as the x2 can be used to specify how the abstraction should be considered.

The English phrase “that I love you” is definitely a sumti, since it’s meant to function as a subject or object in a sentence. It’s also clearly made from an abstraction. It can therefore be translated ''lo su’u mi do prami''. Without the context of the English sentence, though, it’s hard to guess what kind of abstraction was meant. “I will die happy by the time that I love you.” treats the abstraction as an event happening in time. “The truth is that I love you.” treats the abstraction like a bridi, which can be considered true or false. "You don't know how much I love you" treats the (almost same) abstraction as an amount. Using the second sumti place of ''su’u'', these can be explicitly distinguished between:

''lo su’u mi do prami kei be lo fasnu'' is an event.

''lo su’u mi do prami kei be lo bridi'' is a bridi.

''lo su’u mi do prami kei be lo klani'' is an amount.

Using ''su’u'' this way, the semantic, though not grammatical, range of all abstractors can be covered. More usually, though, other abstractors are used. ''nu'', which you also know, treats the abstraction as an event.

__''nu''__ x1 is an event of BRIDI

There are many ways to view an event, and so there are four other abstractors whose semantics are all covered by ''nu'', but more specific.

__''mu’e''__ x1 is a point-like event of BRIDI happening

__''za’i''__ x1 is a state of BRIDI being true

__''pu’u''__ x1 is a process of BRIDI unfolding through stages x2

__''zu’o''__ x1 is an activity of BRIDI consisting of the repeated event of x2

The understanding of these abstractors is tied to the understanding of event contours. ''mu’e'' is akin to the event contour ''co’i'' in the sense that both treat the bridi as point-like in time and space:

''le mu’e mi kanro binxo cu se djica mi'' – ”Me becoming healthy is desired by me” has the semantic meaning that the process of becoming healthy is not being considered. If it consists of chemotherapy, it is plausible that this process is not desired at all. “Becoming healthy”, in a point-like sense is desired, however.

''za’i'' is like the event contour ''ca’o'' in the sense that ''le za’i BRIDI'' begins to apply when the bridi begins and sharply ends when the bridi ceases to be true, much like ''ca’o''. 

''za’o za’i mi kanro binxo'' means that the state of me becoming healthy took too long time; that the time between my health beginning to improve and be actually being healthy was long-winded.

The actual treatment is perhaps better caught by ''pu’u'', which, like event contours in general, puts emphasis on the entire event as unfolding through time. ''.ii ba zi co’a pu’u mi kanro binxo vau .oi'' expresses fear that the painful process of becoming healthy is about to begin. The x2 is filled by a sequence of stages, which can be made by interspacing the stages with the non-logical connective ''ce’o'': ''ze’u pu’u mi kanro binxo kei le nu mi facki ce’o le nu mi jai tolsti ce’o mi renvi'' means “something is a long process of me becoming healthy consisting of the stages A ) I find out B ) something about me begins C ) I endure.”

Finally, the semantics of ''zu’o'' treats the abstraction as consisting of a number of repeated actions: ''lo za'a zo'u darxi lo tanxe cu rinka lo ca mu'e porpi'' – "The observed activity of beating the box caused its current brokenness" is more accurate than the similiar sentence using ''nu'', because ''zu'o'' makes it explicit that it was the repeating of the action of beating, not the beating in itself which broke the box.

The x2 of ''zu'o'' is either one event or a sequence which is repeated. To be unnecessarily explicit, we could have stated that the cause of the current brokenness was ''lo zo'u darxi lo tanxe kei lonu lafti lo grana kei ku ce'o lonu muvgau lo grana lo tanxe kei ku ce'o ...'' and so on.

Note the difference between ''mu’e bajra'', ''za’i bajra'', ''pu’u bajra'', ''zu’o bajra'' and ''nu bajra''. The point-like event of running puts emphasis on the event happening, but nothing else. The state of running begins when the runner begins and stops when the runner stops. The process of running consists of a warm-up, keeping a steady speed, and the final sprint. The activity of running consists the cycles of lifting one foot, moving it forward, dropping it down, repeat with the other foot. All of these aspects are simultaneously covered by the event of running, ''nu bajra''. 

Some abstractions are even more abstract than mere events, which after all are bound in space and time. One example of such is ''li'i'', the "experience abstraction":

__''li'i''__ Experience abstractor: x1 is x2's internal experience of BRIDI

Unlike event abstractions, this is explicitly mental - a ''li'i''-abstraction cannot be said to exist outside the mind of a person. ''li'i'' is derived from ''lifri'', and is always a ''se lifri'' - an experience.

Though it's somewhat related to ''ni'', this might be a good time to introduce ''jei'' - the truth-abstraction. This is one of the least used abstractions of them all, and I only include it here for completeness.

__''jei''__: Truth abstraction: x1 is the truth-value of BRIDI under epistemology x2

A ''jei''-abstraction is something between true and false, and can be represented by a number between 0 (false) and 1 (true). Using ''jei''-abstractions in mathematics is inadvicable, since it hasn't got any properties normally associated with numbers - one might as well represent the truth value on a spectrum of color from red to blue.

''jei'' is rarely used, not because truth abstractions are infrequently needed, but because most lojbanists use other mechanisms to obtain them, for instance ''kau'', as explained later in this lesson.

''mi di'i pensi lo jei mi merko'' - "I often think about whether I am American or not" (contrast with ''mi di'i pensi lo ni mi merko'' - "I often think about how American I am")

The following abstraction is one of the most widely used abstraction due to its frequent usefulness:

__''du'u''__: Bridi abstraction: x1 is the bridi of BRIDI, as represented by text x2

 According to the standard, abstractions like truths, lies, things being discovered or believed are all pure bridi:

''.ui sai pu zi facki le du’u zi citka lo cidjrpitsa'' – “Yes! I just found out that pizza will be eaten soon!”.

 What is being discovered is the truth of an abstract bridi, so ''du'u'' is appropriate.

For bridi to exist (or at least to have any relevance), they must be represented by some text, whether this is speech, thought or writing. The term “text” is misleading if it is expressed only in the mind of someone, but the term nonetheless applies.

One use of the x2 of ''du'u'' is to express indirect quotation:

''.ue do pu cusku ku'i lo se du'u do nelci lo ckafi'' - "Oh! But you said that you liked coffee". Here, the expressed sentence is the text, wherein the bridi is contained.



!!Lojban Lessons - Lesson twenty-nine (semantics of complex abstractions)

All the types of abstraction we have seen thusfar, events and bridi, have all their sumti places filled - if not explicitly, then by ''zo'e''. As we shall see, it's a different story when it comes to the following abstractions. Let's begin with the simplest:



__''ni''__: Amount abstraction: x1 is the amount of BRIDI on the scale x2 



And let's see it put to use:

''mi zmadu do lo ni xekri'' - "I'm blacker than you."

A ''ni''-abstraction is usually some number, exact or inexact. As the following example above shows, what is quantified may not always be practically measurable. In principle, however, blackness could be measured with some optical device. There is some disagreement about whether it's correct to use ''ni'' to quantify something which is unmeasurable, like

''le ni mi pendo do'' - "How much we are friends"



It's wrong to use ''ni'' as a way to enumerate how many objects fit a predicate - it's always about to which extend certain sumti fit a predicate. Thus: ''do mleca mi lo ni se panzi'' means "You are less of a parent than I am", and not "You have fewer children than me".



The abstractor ''ni'' is a great way to get started on the complicated word ''ce'u''.

__''ce'u''__ Pseudo-quantifier binding a variable within an abstraction that represents an open place.

I assume the definition isn't very helpful, so here's a few examples to see it in use:

 ''do mleca mi lo ni ce'u panzi zo'e'' = "You are less than me in quantity: Being a child of someone" = "You are less of a child than I am" 

 ''do mleca mi lo ni zo'e panzi ce'u'' - "You are less than me in quantity: Something being one's child" = "You are less of a parent than I am"

In other words, filling ''ce'u'' in a sumti place inside an abstraction allows the sumti place to remain "open" - not filled by anything, not even a ''zo'e''. This open place is remniscient of the "x"es in the normal English definitions of lojbanic selbri - something __to be filled__ by a sumti. 

For the record, the jufra ''ce'u panzi zo'e'' in the first example actually refers to two distinct bridi: ''mi panzi zo'e'' and ''do panzi zo'e''. Since these two bridi are considered different, the ''zo'e'' need not refer to the same object.

Thus, any abstraction with a ''ce'u'' inside it is a predicate, where the ''ce'u''-places are fillable. Since the abstractors ''ka'' and ''si'o'', is about "fitting a predicate", and since a ''ce'u'' is needed to transform an abstraction into a predicate, all ''ka'' and ''si'o''-abstractions always contain at least one ''ce'u''. A ''ni''-abstraction can contain a ''ce'u'', but may also quantify an abstraction with all the sumti places filled, as in ''li du'e ni do nelci lo vanju''. 

In the abstractions where a ''ce'u'' is present, can the position of the ''ce'u'' be elided, but is then most often assumed to be the first unfilled sumti place. In some contexts, however, the ''ce'u'' can be assumed to be somewhere else, as exemplified with ''mi zmadu do lo ni lo bruna cu jbocre'', where the elided ''ce'u'' is probably hiding in ''lo bruna be ce'u''.



Exactly how the ''ce'u'''d places inside an abstraction relates with the main bridi is specified by the selbri of the main bridi. For ''zmadu'' and ''mleca'', the ''ce'u'''d places are what's quantified by the selbri of the main bridi. The relation is almost always obvious, but as we shall see later, there is one kind of abstraction, whose ''ce'u'' do not relate to the main bridi in any straightforward way.



Before that, though, you need to learn about ''ka'' - probably the abstraction whose understanding has changed the most the recent years. Yet again I remind you that this understanding is not official Lojban, but rather a widespread current understanding. Let's see the official gloss:

__''ka''__ Property/quality abstractor (-ness); x1 is quality/property exhibited by BRIDI.

Under the understanding which I will teach, this gloss is mildly misleading. Instead, ''ka'' should probably be glossed such:

__''ka''__ Predicate abstractor: x1 is the predicate of BRIDI [needs at least one open variable]

Much like a ''ni''-abstraction, a ''ka''-abstraction is a predicate and therefore needs at least one ''ce'u'', often elided. The difference is purely semantic: ''ni'' focuses on how much a certain sumti fits a predicate, whereas a ''ka''-abstraction is the predicate itself. Like with ''ni'', how the ''ce'u''s of ''ka'' relates to the main bridi is defined by the selbri of the main bridi. 

Under this interpretation, ''ka''-abstractions fills most of the sumti places which something is doing or being. Examples are always good:

''mi kakne lo ka '' [ce'u] ''bajra fi lo mi birka'' - "I can run on my arms"

Of course, several ''ce'u'' can be used within a ''ka''-abstraction. What does the following sentence mean?

''mi lo pampe'o cu simxu lo ka ce'u ce'u gletu'' 

Answer: ~~grey,grey:''Me and my lover have sex with each other mutually"~~



The last of the abstractors we treat here is ''si'o''. Like ''ka'', its definition as it will be taught here is different from the official definition. Etymologically, ''si'o'' derives from ''sidbo'', "idea", and the official gloss of ''si'o'' reflects this:

__''si'o''__: Idea/concept abstractor; x1 is x2's concept of BRIDI.

Under the current usage which I will use as standard, a ''si'o''-abstraction is like a ''ka''-abstraction, but with two important differences. 

Firstly, a ''si'o''-abstraction has all its sumti places filled with ''ce'u'' by default, thereby being related less to a specific situation, and more to a general situation. 

Secondly, there is not necessarily any relation between the ''ce'u'' inside the ''si'o''-abstraction and the sumti of the main bridi, and therefore the main selbri does not define this relation.

In order to explain more intuitively the difference between ''ka'' and ''si'o'', consider the following  two bridi:

''mi nelci lo ka ce'u crino'', where the ''ce'u'' refers to a sumti in the outer bridi, namely ''mi'', thus meaning: "I like being green", versus

''mi nelci lo si'o ce'u crino'', where the ''ce'u'' remains completely abstract, making the bridi mean: "I like greenness"



Before we venture on towards the next lesson, there's one word which I think deserves a more thorough explanation: ''kau''.

''kau'' was explained in lesson twelve, but the real implications of it was not. If you have forgotten what it means, I advice you to go back and see. Unfortunately, I can't present a theory on what ''kau'' does when it's present in the main bridi, only on what it does inside an abstraction.

A bridi with abstraction containing a ''kau'' makes two claims: The bridi itself makes one claim as usual, and implicit in the abstraction is furthermore the claim that the word ''kau'' is attached to has a real, nonzero meaning.

This should be demonstrated: The bridi ''mi pu viska lo nu ma kau cliva le salci'' (I saw who left the party) makes two claims. First, it makes an implicit claim that the ''ma'' refers to something real. That is, the bridi actually claims that ''da cliva le salci'' (X left the party). Secondly, the main bridi makes the claim that what the ''ma'' refers to is what was being seen, or in lojban ''mi pu viska lo nu da cliva le salci''. (I saw that X left the party)

This principle is not restricted to the abstractor ''nu'', or to the question word ''ma''. The same principle can be extended to any other abstractor and any other question word, as in the following bridi:

''la .bab. na'e birti lo du'u xu kau la .mias. pampe'o'' (Bob isn't sure whether or not Mia has a boyfriend) states firstly that ''xu'' applies, which means that a truth value correctly can be assigned to the bridi, and secondly that what Bob isn't sure about is the correct truth value for the bridi.

''kau'' can also be applied to a non-question word. This doesn't really change the meaning of the word. The same procedure still applies:

''do ca'o djuno lo du'u la krestcen kau cu cinba la an'' = "You already know that it was Kristian, who kissed Anne." states firstly that ''la krestcen cu cinba la an'' and then that ''do ca'o djuno lodu'u la krestcen cu cinba la an''.



!!Lojban Lessons - Lesson thirty (the not-so-cute assorted words)

Yes, this lesson is yet another which focuses on assorted words. This time, however, the content of the lesson is not chosen by common usage: Unlike words like ''jai'' and ''si'', the following words see little usage in ordinary conversation. Some of them are, however, important to understanding the following lessons, and so these words must be awkwardly placed before their usage in these lessons.



Let us begin with ''xi''; it's easy.

__''xi''__: Subscript. Converts any following number string to a subscript, which has the grammar of an attitudinal (ie. placable practically anywhere).

There are few officially encouraged uses of ''xi'', but precisely because the construct ''xi''+number has the free grammar of an attitudinal, the possible uses of ''xi'' are almost endless. In general, it's used to enumerate any __word__, __variable__ or __grammatical construct__, as opposed to what it refers to. Let's see some examples.

la tsani cu cusku zo coi  .i ba bo la .triliyn. cusku lu .ui coi la tsani coi la klaku li'u  .i ba bo la klaku cu spuda fi lu coi ty. xi pa .e ty. xi re do'u zo'o li'u - "Tsani said "hi", then Triliyn said "Hey Tsani, hey Klaku :)", then Klaku answered "Hello T1 and T2 :P""

Because it's the standard that ''ty.' refers to the last sumti which began with T, ''ty'' by itself as said by Klaku would have referred to Tsani. Two __different__ ''ty.'' can be made by subscripting with ''xi''.

If the rare situation arises that we need more variables of the type ''da'' or ''bu'a'' that there are in the language, an infinite number can be made by simply subscripting any existing with a number. Note that a non-subscripted variable is not defined af being eqiuvalent to any subscripted one. That is: ''ty'' is not always equal to ''ty xi pa'' or ''ty xi no'' or anything of the sort. I expect this to be rarely used, because any sentence with more than 3 ''da''-like words or more than 10 ''ko'a''-like words would be hard to keep track of.



Second, we have ''ki'', of which I am not aware of a singe usage in my time on IRC; probably not because the word's useless, but because few Lojbanic texts are of the kind where you need it.

__''ki''__ "Sticky tense". Set/use tense default; establishes new open scope space/time/modal reference base.

Any row of tense words can be suffixed with ''ki'' to make the tense(s) apply to all following bridi. When, for instance, telling a story, this can be used to make explicit that the default time - the time as meant without any tense words - is the time the story is placed in. Usually, this will not be necessary; beginning a fairytale with ''pu zu vu ku'', one can assume that the entire tale is happening a long time ago and far away. Let's have an example:

''pu zu vu ki ku zasti fa lo pukclite je cmalu nixli goi ko’a  .i ro da poi ''[''pu zu vu'']'' viska ko’a cu nelci ko’a'' - "Once upon a time there was a sweet, little girl. Everyone who saw her liked her". The ''ki'' allows us to elide the three tenses in the second bridi, and in all the bridi to follow.

So, if a bunch of tenses have been make sticky with ''ki'', how do we unstick them? Simple use ''ki'' bu itself, and all sticky tenses are made unsticky.

Lastly, several sets of tenses can be made sticky by subscripting ''ki''. If there are several of such sets in usage at any given time, one can use the subscripted ''ki''s to make the corresponding set of tenses apply. Unsubscripted ''ki'' alone still makes all tense stickiness disappear, so you have to be careful not to use ''ki'' unsubscripted if you plan on using several sets of tenses.



Changing subject. There's a set of sumtcita which are often used, but which I dare not try to define if not under the disclaimer of part three. Let's see official definitions for two of them first.

__''ca'a''__: modal aspect: actuality/ongoing event. Bridi has/is/will happen during under the circumstances of {sumti}

__''ka'e''__: modal aspect: innate capability; possibly unrealized. Bridi is possible under the circumstances of {sumti}

Let's first contrast ''ca'a'' with ''ka'e''. ''ka'e'' means that the bridi is "possible if the event of SUMTI has/is/will occur". ''ca'a'' by contrast, means that the bridi "has, is, or will happen if the event of SUMTI has/is/will occur". 

Like all sumtcita, their corresponding sumti can be elided if the sumtcita is placed before the selbri:

''le vi sovda ka'e fulta .i ja'o bo ri fusra'' - "This egg floats. Therefore, it's rotten".

By using ''ka'e'', this sentence does not state that the egg has floated, or ever will float, but rather that it could float.



__''pu'i''__: modal aspect: can and has; demonstrated potential. Bridi could or could not happen, but in fact it is/did/will happen under the circumstance of {sumti}

__''nu'o''__: modal aspect: can but has not; unrealized potential. Bridi is possible, but is/will/have not happened under {sumti}



Understanding ''ka'e'' and ''ca'a'', ''nu'o'' simply means ''ka'e je na ku ca'a'', and ''pu'i'' means ''ca'a je ka'e na ku''. 

Historically, these four words was tense sumtcita - therefore the "modal aspect" in their definitions. All tense sumtcita was then not considered sumtcita at all, but rather "selbri tcita". A modern understanding of Lojban is gaining popularity, wherein the tense sumtcita are considered sumtcita, almost exactly like the BAI, and in where selbri tcita are not used. 

Because of these four words' history as selbri tcita, they can be freely elided - indeed, since one of the four words always applies, one is always assumed to be elided. This is most often ''ca'a''. Indeed, it's so often ''ca'a'' that one could wonder why ''ca'a'' is not the default.

One reason is that some selbri has two useful definitions, one which implies ''ka'e SELBRI'' and one which implies ''ca'a SELBRI''. For an example, see ''fasnu'', which can mean "x1 is happening" or "x1 is an event", where the first implies ''ca'a fasnu'' and the second ''ka'e fasnu''

Another use of "implied ''ka'e''" is as a way to escape an annoying philosophical problem in the language. A selbri only applies if all its places apply too. For some selbri, like ''kabri'', that's a problem.

__''kabri''__ x1 is a cup containing contents x2 and of material x3

The definition suggests that if the content of the cup is removed, the x2 no longer applies and it stops being ''lo kabri''. Implied ''ka'e'', or more fittingly, ''nu'o'', let us escape that problem.





!!!End of lessons

Sorry, but as of now, there are no more lessons in this series. Perhaps more will be added later. Meanwhile, feel free to visit ((wavelessonscontinued|the first part of Wavelessonscontinued)) or ((wavelessonscontinued|The second part of Wavelessonscontinued)).


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