Friendly Lojban
Chapter 8. Connecting Ideas
The Four Basic Logical Operations
Lojban has a systematic set of words for connecting two claims logically. The logic is truth-functional: the truth or falsehood of the combined claim depends only on the truth or falsehood of the parts.
Four basic operations cover almost all everyday needs:
| Symbol | Operation | Truth table | Plain English |
|---|---|---|---|
| A | or (inclusive) | TTTF | at least one is true |
| E | and | TFFF | both are true |
| O | if and only if | TFFT | either both or neither |
| U | whether or not | TTFF | first is true regardless |
Reading truth tables: the four rows represent the four cases (TT, TF, FT, FF — first-true/second-true, first-true/second-false, etc.). The result column shows whether the combined claim is true in each case.
So A (or) is true in three of four cases — whenever at least one component is true. E (and) is only true when both are true. O (iff) is true when both match.
Connecting Whole Sentences (ijeks)
The simplest connection is between two complete sentences. The connective goes between them, starting with .i:
| ijek | Operation | Example |
|---|---|---|
| .ije | and | A and B |
| .ija | or | A or B |
| .ijo | iff | A if and only if B |
| .iju | whether or not | A whether or not B |
la .alis. cu klama .ije la .djan. cu cadzu Alice comes and John walks.
mi citka lo plise .ija mi citka lo perli I eat an apple or I eat a pear.
mi gleki .iju do klama I'm happy whether or not you come.
Negating inside the connective:
Add na before the vowel to negate the first sentence's contribution; add -nai after the vowel to negate the second:
mi citka .ijanai mi pinxe I eat or I don't drink. (= "I eat if I drink")
mi citka .inaja mi pinxe I don't eat or I drink. (= "If I eat, then I drink")
The most useful derived form is .inaja (if-then, material conditional):
mi klama .inaja do klama If I go, then you go.
Forethought Connection: ga … gi
The afterthought form above adds the connective after the first sentence. The forethought form signals the connection before the first sentence:
| Forethought | Meaning |
|---|---|
| ga … gi | either … or … |
| ge … gi | both … and … |
| go … gi | … iff … |
| gu … gi | … whether or not … |
| ganai … gi | if … then … |
ge la .alis. cu klama gi la .djan. cu cadzu Both Alice comes and John walks.
ga mi citka gi mi pinxe Either I eat or I drink.
ganai mi klama gi do klama If I go, then you go.
Forethought is stylistically cleaner for if-then constructions, since it avoids the appearance of asserting the first sentence and then qualifying it.
Connecting Sumti (eks)
To connect two arguments (rather than whole sentences), use eks — bare vowel letters (possibly with na/nai):
| ek | Meaning |
|---|---|
| .a | or |
| .e | and |
| .o | iff |
| .u | whether or not |
la .alis. .e la .djan. cu klama Alice and John come.
mi citka lo plise .a lo perli I eat an apple or a pear.
mi tavla la .alis. .e la .djan. I talk to Alice and to John.
Note: .e between sumti is not the same as .ije between sentences. la .alis. .e la .djan. cu klama means "Alice comes and John comes (separately)" — it expands to two bridi. You cannot use .e to mean "together" — that would be joi (see below).
Connecting Selbri (jeks)
To connect two relation words (selbri) in a single bridi, use jeks — formed with j + vowel:
| jek | Meaning |
|---|---|
| ja | or |
| je | and |
| jo | iff |
| ju | whether or not |
la .teris. cu tirxu je blabi Terry is a tiger and white. (= both a tiger and white)
le mlatu cu melbi ja pluka The cat is beautiful or pleasant.
mi sutra je clani I am fast and tall.
Jeks are most commonly seen as je, connecting two properties of the same x₁.
Non-Logical Connectives
Not every "and" is logical. Sometimes you want to say things are together or form a sequence rather than just both being true:
- joi — "in a mass together with"
- Combines two sumti into a joint mass acting as one.
mi joi do cu bevri le pipno You and I (together as a unit) carry the piano. (neither of us alone)
joi is the connective behind mi'o (= mi joi do). It's used when the components cooperate as a collective, not when each individually satisfies the relation.
- jo'u — "jointly, in common"
- Expresses a shared relationship.
mi jo'u do cu simxu le ka prami You and I mutually love (each other).
- ce — "and (in a set)"
- Creates a set sumti from two members.
mi ce do cu gunma You and I form a group/set.
- fa'u — "respectively"
- Parallel assignment — first to first, second to second.
la .alis. fa'u la .djan. cu klama fa'u cadzu Alice goes, John walks (respectively). (Alice-goes, John-walks in parallel)
Connecting in Context: Scope
When you connect in different positions, the scope changes:
Sentence-level (.ije):
mi klama .ije do cadzu I go and you walk. (two independent claims)
Sumti-level (.e):
mi .e do cu klama I and you go. (same claim, both of us going)
Selbri-level (je):
mi klama je cadzu I go and walk. (I do both to the same destination)
All three are logically equivalent when the sumti/selbri being connected share all other slots — but they differ in emphasis and brevity.
The to'e Opposite
A useful related particle: to'e placed before a selbri or brivla gives its opposite:
to'e melbi ugly (opposite of beautiful)
to'e klama not-going / staying away
to'e is not a connective but pairs well with je:
le zarci cu barda je to'e melbi The store is big and ugly.
na'e and No'e: Scalar Negation
Related to negation and connection, these words mark positions on a scale:
- na'e — "other than, non-"
- x₁ is not the default value; some other value holds.
mi na'e klama I do something other than go. (not necessarily the opposite — maybe I stay, maybe I run)
- no'e — "midpoint, neutral"
- Approximately the middle of the scale.
le cukta cu no'e barda The book is medium-sized. (neither big nor small)
to'e — opposite end of the scale.
These three together form a scalar system: no'e (neutral) → na'e (non-default) → to'e (opposite). Full negation logic is covered in Chapter 13.
Why Are There Six Connective Positions?
This is a grammar-derived question that trips up many learners. The answer is that each connective position corresponds to a different level in the parse tree. Using the wrong class at a given level either produces a grammar error or silently changes the meaning.
Here is the full map:
| Level | cmavo class | Connects | Example |
|---|---|---|---|
| Between full sentences | ijek (.ije, .ija…) | bridi + bridi | mi klama .ije do cadzu |
| Between bridi-tails (same x₁) | gihek (gi'e, gi'a…) | predicate+args, sharing x₁ | mi klama gi'e cadzu |
| Between sumti | ek (.e, .a…) | sumti + sumti | mi .e do cu klama |
| Within tanru (selbri) | jek (je, ja…) | brivla + brivla | mi tirxu je blabi |
| Forethought (before both) | gek (ge…gi, ga…gi…) | both bridi together | ge mi klama gi do cadzu |
| Forethought within selbri | guhek (gu'e…gi, gu'a…gi…) | both selbri together | mi gu'e tirxu gi blabi |
Why it matters — two examples that look similar but mean different things:
mi .e do cu klama — x₁ = [mi and do]; one bridi, we both go mi klama .ije do klama — two separate bridi; I go, and you go
Both translate as "I and you go" in English, but they are grammatically different. The .e version has a compound x₁; the .ije version makes two independent claims.
mi klama je cadzu le zarci — I go-and-walk to the store (both go and walk, same destination) mi klama .ije mi cadzu le zarci — I go to the store. I walk to the store. (two claims)
The gihek shortcut: When the same x₁ does two things, gi'e is more concise than .ije:
mi klama le zarci gi'e facki lo cukta I go to the store and find a book. (same I, two actions)
This is shorter than mi klama le zarci .ije mi facki lo cukta and explicitly marks that the same x₁ is doing both things.
Chaining several tails: giheks associate left to left — each new tail still shares the same x₁, but may introduce its own trailing sumti:
mi klama le zarci gi'e cadzu le dargu gi'e pinxe lo jisra I go to the store, walk on the road, and drink the juice. (one mi, three predicates)
The first place of cadzu is the walker (mi); le dargu is the route. If a later tail needs a different x₁, you cannot use gihek — split into .ije sentences or rephrase.
Forethought: The ge…gi family signals the connective before the first element. This is useful when you want "if-then" without apparently asserting the antecedent:
ganai mi klama gi do klama — If I go, then you go.
Compare to the afterthought .inaja, which puts the connective between them — by the time you hear the connective, the first claim has already been made.
Where to go next (tense, modals, mekso, abstractions)
Logical connectives interact with other grammar in dedicated sections:
| Topic | Chapter |
|---|---|
| Tense + connective (.i + tense + jek) — I went, then you go | 16 — Tenses and Logical Connectives |
| Modal + mixed connective — .ijeki'ubo and friends | 10 — Modals |
| Abstractors connected with joi / .e | 12 — Abstractor Connection |
| Connectives inside mekso (operands / operators) | 18 — Mekso |
Grouping Afterthought Connectives: bo
Afterthought connectives follow the left-grouping rule: A .ije B .ije C = (A and B) and C. When you want different grouping — A and (B or C) — append bo to the connective that should bind tighter:
mi nelci la djan. .ije mi nelci la martas. .ijabo mi nelci la meris. I like John, and (I like Martha or I like Mary).
The .ijabo binds the Martha/Mary clause first. Without bo, .ija would left-group with the previous .ije.
The same works for sumti connectives:
mi dzukla le zarci .e le zdani .abo le ckule I walk to the market and (the house or the school).
For bridi, explicit parentheses with tu'e…tu'u are clearer for complex nesting:
tu'e mi cinba do .ije do cinba mi tu'u .ijo tu'e mi prami do .ije do prami mi (I kiss you and you kiss me) if-and-only-if (I love you and you love me).
Key rules for bo-grouping:
- bo after a connective = bind tighter than unmarked connectives
- Multiple consecutive bo-marked connectives = right-grouping among themselves
- For three or more clauses, tu'e…tu'u (sentences) or ke…ke'e (sumti/tanru) are cleaner
Termsets: Connecting Multiple Places at Once
When two bridi differ in more than one sumti simultaneously — not just one argument but two — termsets let you connect them compactly.
A termset groups terms together using ce'e (selma'o CEhE) between them. The logical connective is prefixed by pe'e (selma'o PEhE):
mi klama le zarci ce'e le briju pe'eje le ckule ce'e le zdani I go [to the market from the office] and [to the school from the house].
The pairs le zarci + le briju (destination + origin) and le ckule + le zdani are the two termsets. Without ce'e, linking the sumti separately would be ambiguous about which destination pairs with which origin.
Expanding shows what this means:
mi klama le zarci le briju .ije mi klama le ckule le zdani I go to the market from the office, and I go to the school from the house.
Forethought termsets use nu'i (opening bracket) and nu'u (closing bracket, elidable), with a gek inside:
mi klama nu'i ge le zarci le briju nu'u gi le ckule le zdani I go [both to the market from the office] [and to the school from the house].
Termsets appear in several other contexts too: in tense coordination (CLL §10.25) and quantifier scope (CLL §16.7).
Connective Questions: ji, je'i, gi'i, ge'i, gu'i
To ask which connective applies between two things — not just whether the combined statement is true, but what the logical relationship is — Lojban uses special question cmavo that stand in for a connective:
| cmavo | selma'o | Use |
|---|---|---|
| ji | A | sumti connective question |
| je'i | JA | tanru connective question (between selbri units) |
| gi'i | GIhA | bridi-tail connective question |
| ge'i | GA | forethought bridi connective question |
| gu'i | GUhA | forethought tanru connective question |
do djica loi ckafi ji loi tcati Do you want coffee [what-connective?] tea?
A yes/no question with xu would ask whether a specific relationship holds. A ji question asks you to specify the connective. Possible answers:
.e — both coffee and tea .a — either one (you choose) .onai — one but not both (exclusive or)
la .alis. gerku gi'i mlatu Is Alice a dog [what-connective?] a cat?
Answers: gi'enai (dog but not cat), nagi'e (cat but not dog), nagi'enai (neither), gi'e (both — unusual but possible). The answer nagi'o ("one or the other but I won't say which") is technically valid but uncooperative.
je'i asks which JA cmavo belongs between two tanru pieces (the same slots where je, ja, jonai, … appear):
mi sutra je'i masno cadzu I quickly [which connective?] slowly walk?
Plausible answers: je (both modifiers apply), ja (one or the other), jonai (exactly one), and so on — each is a bare JA, like answers to ji/gi'i.
ge'i and gu'i ask which GA or GUhA starts a forethought connection. They are grammatical, but you should not answer with an isolated ge/gu'e/ga/gu'a … — that would sound like the beginning of a new forethought bridi. Use the afterthought connective instead (e.g. .e, gi'e, je); the connective questions summary is above in Chapter 8.
ge'i mi klama le zarci gi mi klama le zdani [Which GA?] I go to the market, I go to the house?
gu'i sutra gi masno cadzu [Which GUhA?] quick, slow walk? (forethought version of the je'i pattern above)
The answer to ji / je'i / gi'i is simply the bare connective — grammatically valid on its own. For ge'i / gu'i, prefer the same connective in afterthought shape.
Interval Connectives: bi'i, bi'o, mi'i
The selma'o BIhI provides three connectives for specifying intervals — ranges between two endpoints. These are non-logical connectives used in the same positions as JOI.
| cmavo | Meaning | When to use |
|---|---|---|
| bi'i | unordered interval (between) | endpoints are interchangeable |
| bi'o | ordered interval (from…to) | order matters (direction/time) |
| mi'i | center-and-radius interval | one point + distance |
bi'i (order doesn't matter):
mi ca sanli la drezdn. bi'i la frankfurt. I am standing between Dresden and Frankfurt.
The interval is symmetric — "between Dresden and Frankfurt" = "between Frankfurt and Dresden."
bi'o (order matters):
mi cadzu ca la pacac. bi'o la recac. I walk from 1 o'clock to 2 o'clock.
Here la pacac. must come before la recac. — reversing them gives an 11-hour interval. Use sebi'o to reverse the direction: from 2 to 1.
mi'i (center + radius):
le jbama pu daspo la .uacintyn. mi'i lo kilto be li mu no The bomb destroyed [an area centered on] Washington within 50 km.
Endpoint inclusion: ga'o and ke'i
By default, bi'i/bi'o are ambiguous about whether the endpoints are included. The GAhO cmavo specify this:
| cmavo | meaning |
|---|---|
| ga'o | closed/inclusive (endpoint is included) |
| ke'i | open/exclusive (endpoint is excluded) |
They appear on both sides of the BIhI cmavo, each applying to the adjacent endpoint:
la drezdn. ga'o bi'i ga'o la frankfurt. Between Dresden and Frankfurt, inclusive of both endpoints.
la drezdn. ke'i bi'i ke'i la frankfurt. Strictly between Dresden and Frankfurt, excluding both cities.
la pacac. ga'o bi'o ke'i la recac. From 1 o'clock (inclusive) to 2 o'clock (exclusive). (the hour doesn't include its endpoint)
A negated interval with -nai means everything outside that range:
do dicra .e'a mi ca la daucac. bi'onai la gaicac. You may disturb me at times outside 10–8 (i.e., not during those hours).
Summary
Cross-links: tense + connective → Ch.16; modal + .ije… → Ch.10; mekso → Ch.18; abstractor connection → Ch.12.
Sentence connectives (ijeks): placed between full bridi
- .ije = and; .ija = or; .ijo = iff; .iju = whether-or-not
- .inaja = if-then (negate first); .ijanai = or-not-second
Bridi-tail connectives (giheks): share x₁ between two predicates
- gi'e = and; gi'a = or; gi'o = iff; gi'u = whether-or-not
- Chains (gi'e … gi'e …) = several tails for one x₁; each tail may have its own following sumti
Forethought connectives (geks): signal connection before first bridi
- ge…gi = both…and; ga…gi = either…or; ganai…gi = if…then
Forethought selbri (guheks): forethought within tanru
- gu'e…gi = both…and; gu'a…gi = either…or
Sumti connectives (eks): between arguments
- .e = and; .a = or
Selbri connectives (jeks): between relation words
- je = and; ja = or
Non-logical: joi (mass together), jo'u (jointly), ce (set-forming), fa'u (respectively)
Scalar: na'e (non-), no'e (middle), to'e (opposite)
Grouping afterthought connectives:
- Default is left-grouping: A .ije B .ije C = (A and B) and C
- bo appended to a connective binds tighter: .ijabo = bind-right
- tu'e…tu'u = explicit bridi parentheses for complex nesting
Termsets (connecting multiple places at once):
- ce'e = joins terms within one termset; pe'e + jek = the connective
- nu'i…nu'u = forethought termset brackets
Connective questions (ask which connective, not truth value):
- ji (A) = sumti connective question: coffee ji tea?
- je'i (JA) = tanru connective question (mi sutra je'i masno cadzu)
- gi'i (GIhA) = bridi-tail connective question
- ge'i (GA) / gu'i (GUhA) = forethought connective questions; answers use afterthought connectives (see section above)
- Answer with a bare connective: .e, gi'enai, je, …
- Full question-answer protocol (including ma fa'u ma): Chapter 17
Interval connectives (selma'o BIhI — non-logical):
- bi'i = unordered interval (between); endpoints interchangeable
- bi'o = ordered interval (from…to); sebi'o = reversed
- mi'i = center-and-radius interval
- ga'o = inclusive endpoint; ke'i = exclusive endpoint
- bi'onai = everything outside the interval