Chapter 12. Abstractions#

The Core Idea#

Lojban lets you take an entire bridi — a whole claim — and treat it as a thing: an event, a property, a proposition, a quantity. This is called abstraction, and it's done by prefixing a bridi with one of the NU particles.

Without abstractions, you can say mi klama le zarci (I go to the store). With abstraction, you can wrap that up and talk about the going:

le nu mi klama le zarci the event of my going to the store

This abstract sumti can now go in any slot of another bridi:

le nu mi klama le zarci cu pluka The event of my going to the store is pleasant.

mi nelci le nu mi klama le zarci I like the event of my going to the store. → I like going to the store.

The bridi inside an abstraction is closed by kei (elidable terminator). When the abstraction ends the sentence or is followed by cu, kei can usually be omitted.

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nu: Events#

nu is the general event abstractor — the most common NU.

nu

x₁ is an event/state described by the bridi

le nu la .teris. cadzu the event of Terry walking

le nu do klama cu ckape The event of you coming is dangerous.

Lojban "events" in this sense can be brief (a kiss) or lifelong (breathing). nu doesn't care — it just packages the bridi as a thing that happened / is happening / will happen.

Four refined event abstractors:

mu'e

point-event — the bridi seen as a single unstructured moment

pu'u

process — structured event with beginning, stages, end

zu'o

activity — repetitive or cyclic event

za'i

state — condition that either holds or doesn't

le mu'e la .djan. catra la .djim. the (point-event) of John killing Jim — seen as instantaneous

le pu'u le latmo balje'a cu porpi the process of the Roman Empire falling apart — structured and extended

mi tatpi ri'a le zu'o mi plipe I'm tired because of the activity of jumping.

le za'i mi jmive cu ckape do The state of my being alive is dangerous to you.

All four can be replaced by bare nu with some loss of precision.

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ka: Properties#

ka abstracts a property — a quality that things can have or lack.

ka

x₁ is the property described by the bridi

Properties are used to fill quality-slots in many gismu:

do cnino mi le ka xunre You are new to me in the quality of being red. → Your redness is new to me.

mi zmadu do le ka clani I exceed you in the property of being tall. → I am taller than you.

ce'u marks the "open slot" of the property — the thing that has the property:

le ka ce'u clani the property of being tall (ce'u = the thing that is tall)

When the open slot is x₁ (default), ce'u can be omitted. But when it's in another position, you need it:

le ka mi prami ce'u the property of being loved by me (ce'u = the thing loved)

le ka ce'u prami mi the property of loving me (ce'u = the lover)

These two properties are very different! The explicit ce'u prevents ambiguity.

Two ce'u = a relationship abstraction (rare but valid):

le ka ce'u prami ce'u the relationship of loving

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du'u: Propositions#

du'u abstracts a proposition — a claim that is either true or false.

du'u

x₁ is the proposition that [bridi]

Use du'u when you want to talk about a claim as a fact (something known, believed, said, etc.):

mi djuno le du'u do klama I know the proposition that you are going. → I know that you are going.

mi jinvi le du'u le mlatu cu melbi I believe the proposition that the cat is beautiful. → I think the cat is beautiful.

la .alis. cusku le du'u mi cadzu Alice says the proposition that I walk. → Alice says that I walk.

du'u vs nu: Use du'u for mental and verbal acts (knowing, believing, saying, claiming). Use nu for physical/experiential events (seeing, hearing, doing, liking in a sensory way):

mi djuno le du'u do klama — I know that you're going. (proposition) mi viska le nu do klama — I see the event of you going. (event/perception)

du'u vs jei: du'u is the claim; jei is the truth value (how true the claim is, including fuzzy “shades”). Curiosity or doubt often fits jei better than plain du'u:

mi kucli le du'u la .frank. cu bebna I'm curious whether Frank is a fool.

mi kucli le jei la .frank. cu bebna I'm curious how true it is that Frank is a fool.

Truth still lives in the outer predicate: mi djuno le du'u … only works for facts you actually know; the abstraction itself does not “contain” truth.

x₂ of du'u — linguistic form: du'u has a second place: a piece of language that expresses the bridi. le se du'u (or le se du'u … with the predication filled) is the usual sumti when someone said something equivalent to a claim without quoting exact words:

la .djan. cusku le se du'u la .frank. cu bebna John says something to the effect that Frank is a fool.

That differs from lu … li'u, which asserts he used those exact Lojban words.

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ni: Amounts#

ni abstracts a measurable quantity:

ni

x₁ is the amount/degree of [bridi]

le ni le pixra cu blanu the amount of the picture being blue → how blue the picture is

mi zmadu do le ni mi clani I exceed you in how tall I am. → I am taller than you. (comparing amounts)

ni only makes sense with measurable properties. "The amount of Jane being a mother" (le ni la .djein. mamta) is meaningless — motherhood isn't measurable on a scale.

ka vs ni:

le pixra cu cenba le ka ce'u blanu The picture varies in the property of being blue. (blueness comes and goes — yes/no)

le pixra cu cenba le ni ce'u blanu The picture varies in how blue it is. (the degree of blueness changes)

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jei: Truth Values#

jei abstracts the truth value of a proposition — is it true or false, and to what degree?

le jei li re su'i re du li vo the truth value of 2+2=4 → evaluates to "true"

jei is most useful in fuzzy contexts where truth admits degrees, or when you want to explicitly handle truth as a value:

le jei do klama the truth value of whether you are going

mi djuno le jei do klama I know whether you are going.

jei has an x₂ place (like ni) for the scale or standard of “how true” — important in fuzzy logic; everyday speech often leaves it implicit.

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si'o: Concepts / Ideas#

si'o abstracts a concept or idea as it exists in someone's mind:

le si'o lo prenu cu simxu prami the concept of people loving each other

mi nelci le si'o la lojban. I like the idea of Lojban.

si'o is used for mental representations, ideals, and the conceptual content of thoughts — more subjective than du'u.

x₂ place: x₁ is the concept [bridi]; x₂ is who holds it — a person, a community, or a “mind” in the broad sense. When you fill x₂, close the abstraction bridi with kei first, then be:

le si'o lo prenu cu simxu prami kei be la .teris. The concept of people loving each other, as Terry conceives it.

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Indirect Questions with kau#

Recall from Chapter 6 that kau marks the questioned element in an indirect question. The containing abstractor is usually du'u:

mi djuno le du'u ma kau klama I know who is going. (ma kau = the questioned element)

mi djuno le du'u xu kau do klama I know whether you are going.

mi na djuno le du'u do klama ma kau I don't know where you are going.

Without kau, the question word is direct. With kau, the whole thing becomes an embedded indirect question.

Why kau? Inside le du'u, a bare ma (or other question fragment) still parses as a direct question — Who is it that I know goes? — not as an indirect “I know who goes.” kau marks the questioned piece as the answer sought in the embedded reading.

Sometimes you can avoid kau: when the questioned part is a sumti, djuno’s fi place can carry “what is known about X”:

mi djuno fi le pu klama be le zarci I know something about the past goer to the store — often glossed as *I know who went._

That paraphrase is loose: the listener must infer that identity is what is known, not (say) the person’s shoe size. When the questioned bit is not a sumti — for example, a connection or operator — le du'u … kau is usually the only clean option.

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Sumti Raising: tu'a and jai#

Sometimes a gismu's place structure requires an event or property abstraction, but you want to use a plain sumti. tu'a and jai help bridge this gap.

tu'a — "some event or fact about [sumti]"

An informal sumti-raiser. Instead of constructing a full abstraction, wrap the relevant sumti in tu'a:

mi djica tu'a do I want something involving you. (≈ I want you to do something)

mi djica le nu do klama (full version) I want the event of you coming.

tu'a do ≈ le nu do co'e (some unspecified event about you). It's much shorter and is natural in speech.

mi troci tu'a le kabri I try something with the cup. (≈ I try to lift / fill / clean it — context decides)

jai + modal — the precise alternative

jai promotes the tag argument of a modal to x₁ of the selbri. This is the formal mechanism behind sumti-raising:

le nu mi djica cu jai mu'i klama fai mi My wanting is the motivation for the going, which I do.

Here the event "my wanting" is raised to x₁, and the original x₁ (mi) is displaced to fai (the special place created by jai). In practice, tu'a handles most casual sumti-raising; jai is for precise grammatical control.

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Lojban Sumti Raising with ni and li'i#

Two other abstractors interact with sumti-raising:

ni — "the amount/degree that"

Used with quantity-predicates like barda (big), melbi (beautiful), zmadu (exceeds):

le ni le zdani cu barda the amount of the house's bigness = the house's size

mi zmadu do le ni mi barda I exceed you in the amount that I am big. = I am bigger than you.

This is Lojban's way of making scalar comparisons exact.

li'i — "the experience of"

Abstracts a subjective experience:

le li'i mi cortu cu pluka nai The experience of my being in pain is not pleasant.

li'i is used when the experiential quality matters, not just the event.

x₂ place: x₁ is the experience of [bridi]; x₂ is the experiencer. Example with kei be:

mi morji le li'i mi verba kei be mi I remember my experience of being a child.

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su'u: The General Abstractor#

su'u is a "catch-all" abstractor — it abstracts without specifying what kind of abstraction applies. Its unique feature is an x₂ place that lets you specify the abstraction type explicitly:

x₁ is the [x₂-type] abstraction of [bridi]

Examples:

le su'u le ci smacu cu bajra The abstract nature of the three mice running. (type unspecified — "See how they run!")

le su'u mi klama kei be lo fasnu The event-abstraction of my going. (x₂ = lo fasnu specifies it's an event, same as le nu mi klama)

su'u can substitute for any other abstractor when you want to be vague or when no existing abstractor fits:

le su'u la .iecuas. cu jmive The abstract nature of Jesus's living. (neither event, property, nor amount — something more like "the mystery/fact of")

Important: when filling the x₂ place, use kei be to close the abstraction bridi first:

le su'u mi klama kei be lo fasnu ✓ le su'u mi klama be lo fasnu ✗ (the be attaches inside the bridi, modifying klama)

The same kei be pattern applies whenever you specify x₂ on su'u, si'o, or li'i (and similarly for other abstractors with an outer be): without kei, be is read as part of the inner bridi, not as tagging the abstractor’s second place.

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Event Abstractors and ZAhO Tenses#

The four NU event-type abstractors (nu, pu'u, za'i, zu'o, mu'e) have a systematic correspondence with the ZAhO event-contour tenses. The ZAhO cmavo describe which phase of an event the bridi refers to.

The ZAhO cmavo#

Which ZAhO apply to which event types#

Not all ZAhO make sense with all NU types:

Examples in use:

mi co'a citka le sanmi I start eating the meal. (co'a = beginning edge of the eating event)

mi ca'o citka le sanmi I am in the middle of eating the meal. (ca'o = ongoing process)

mi ba'o citka le sanmi I have finished eating the meal. (ba'o = after-the-event perspective)

mi za'o citka le sanmi I am still eating the meal past its natural end. (za'o = excessive continuation)

mi co'i citka le sanmi I eat the meal. (as a completed achievement; the whole event as a point)

The ZAhO tenses are placed in the normal tense slot before the selbri. They can be combined with PU tenses:

mi pu co'a citka I had just started eating. (in the past, at the starting edge)

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Abstractor Connection#

Abstractors themselves can be connected with logical connectives, just like selbri:

le nu joi ka la .alis. cu klama the event and/or property of Alice's going

Purely logical connection between abstractors of the same type is also possible — two events, two properties, etc.:

le nu mi cadzu .e le nu do bajra the event of my walking and the event of your running

joi (non-logical connective: "combined mass") combines two abstractions:

le nu .e ka do cadzu the event and property of your walking

This is advanced and rare, but useful when you need to speak about multiple aspects of the same bridi simultaneously.

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Comparative lujvo (-mau, -me'a)#

“More than” / “less than” often use lujvo ending in -mau (zmadu) and -me'a (mleca) instead of bare zmadu/mleca — the places are easier to fill.

mi citmau do lo nanca be li xa I am six years younger than you. (citno + zmadu)

do citme'a mi lo nanca be li xa You are six years less young than me. (parallel mleca form)

Packed comparatives like nelcymau (like-more) and klamau (go-more) follow regular place conventions: the two things compared usually line up with the first places of the embedded relation. The forms and their places:

For “more than before” without naming a rival, use increase/decrease (zenba, jdika) rather than an empty zmadu second place. Compare:

mi ca tsamau I'm stronger now — but tsamau is still a -mau comparative; z₂ is often read as “than someone,” not “than before.”

mi ca tsaze'a I increase in strength. → I'm stronger now (no unnamed rival).

traji superlatives (citrai, balrai, …) pick the extreme member of a set:

la djudis. cu citrai lo'i lobypli Judy is the most expert Lojbanist.

la .ainctain. cu balrai lo'i skegunka Einstein is the greatest scientist. Tanru-style comparatives in depth: Chapter 15.

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Summary of NU Abstractors#

Key rules:

• Abstractions are closed by kei (elidable at end or before cu)
• ce'u marks the open slot in ka (and sometimes ni) abstractions
• Use du'u for knowing/believing/saying; nu for events you perceive/cause
• kau in a du'u abstraction creates an indirect question
• tu'a = quick sumti-raiser (some event about [X]); jai = precise promotion via modal

su'u — the general/vague abstractor:

• x₁ is the [x₂-type] abstraction of [bridi] — type specified in x₂
• Use when no other NU fits, or to be deliberately vague about abstraction type
• kei be required to close the bridi before filling x₂: le su'u … kei be lo fasnu
• du'u also has an x₂ (linguistic expression); see le se du'u above

ZAhO event contours (tense aspect particles):

• pu'o = before event; ca'o = during; ba'o = after
• co'a = starting edge; co'u = ending edge; co'i = whole event as point
• de'a = temporary pause; di'a = resumption; mo'u = natural end; za'o = past natural end
• Combine with PU: pu co'a = had just started
• ZAhO applicability by event type: pu'u (process) takes all; za'i (state) no za'o/mo'u; zu'o (activity) no sharp start/end; mu'e (point) no ca'o