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Logical connectives 1

If you ask a Lojbanist: Do you want milk or sugar in your coffee? She'll answer: Correct.

Witty as this joke might be, it illustrates a weird property of the English way of asking this question. It is phrased as a true/false question, but it really isn't. In Lojban, we can't have this kind of inconsistency, and so we must find another way of asking this kind of question. If you think about it, it's pretty hard to find a good and easy way, and it seems Lojban has picked a good way instead of an easy way.

To explain it, let us take two separate bridi:

  1. I like milk in my coffee.
  2. I like sugar in my coffee.

Both of these bridi can have the state true or false. This yields four combinations of which bridi is/are true:

  • A) 1 and 2
  • B) 1 but not 2
  • C) 2 but not 1
  • D) neither 1 nor 2

I, in actuality, like milk in my coffee, and I'm indifferent as to whether there is sugar in it or not. Therefore, my preference can be written A) true B) true C) false D) false, since both A and B yields true for me, but neither C nor D does.

A more compact way of writing my coffee preferences would be TTFF for true, true, false, false. Similarly, a person liking his coffee black and unsweetened would have a coffee preference of FFFT. This combination of "true" and "false" is called a truth function, in this case for the two statements "I like milk in my coffee" and "I like sugar in my coffee". Note that the order of the statements matters.

In Lojban, we operate with four truth functions, which we consider fundamental:

  • A: TTTF (and/or)
  • O: TFFT (if and only iff)
  • U: TTFF (whether or not)
  • E: TFFF (and)

In this example, they would translate to something like: A: "Sugar and/or milk (just not black and unsweetened)"; O: "Either both milk and sugar, or none of the two"; U: "Milk, and I don't care about if there's sugar or not"; and E: "Milk and sugar, please". A truth function of "TTTT" (which is not among the fundamental ones) would mean "Whatever, any coffee will do".

In Lojban, you place the word for the truth function between the two bridi, selbri or sumti in question. That word is called a logical connective. The words for truth functions between sumti (and just for sumti!) are .a, .o, .u and .e. How nice. For instance: "I like dogs and cats" would be "mi nelci lo gerku .e lo mlatu".

Here are a few examples:

Sentence Possible translation
mi .e do ba tavla I will talk, and you will talk.
mi .o do ba tavla I will talk, if and only if you will talk.
mi .u do ba tavla I will talk, regardless of whether you talk.
mi .a do ba tavla I will talk and/or you will talk.

You can perhaps deduce that there are sixteen possible truth functions. We will later see how to transform the four fundamental ones to obtain the other twelve.

Additionally, it is possible to logically connect not only sumti, but also selbri and even bridi. This will also be covered in a future lesson.


As usual, before proceeding to the next lesson, get some practice with interactive exercises – look for the "Practice" button nearby!

Beware that exercises loop indefinitely, so feel free to stop once you feel you've had enough. And be sure to revisit exercises on different days, to benefit from the spacing effect.

Lesson plan

  • Lesson
    • Logical sumti connectives: .a, .e, .o, .u
  • New exercises


dunda x1 [donor] gives/donates gift/present x2 to recipient/beneficiary x3 [without payment/exchange]

pelxu x1 is yellow/golden [color adjective]

zdani x1 is a nest/house/lair/den/[home] of/for x2

tavla x1 talks/speaks to x2 about subject x3 in language x4

pendo x1 is/acts as a friend of/to x2 (experiencer); x2 befriends x1

prenu x1 is a person/people (noun) [not necessarily human]; x1 displays personality/a persona

mlatu x1 is a cat/[puss/pussy/kitten] [feline animal] of species/breed x2; (adjective:) x1 is feline

ctuca x1 teaches audience x2 ideas/methods/lore x3 (du'u) about subject(s) x4 by method x5 (event)

nelci x1 is fond of/likes/has a taste for x2 (object/state)

gerku x1 is a dog/canine/[bitch] of species/breed x2

melbi x1 is beautiful/pleasant to x2 in aspect x3 (ka) by aesthetic standard x4

sutra x1 is fast/swift/quick/hastes/rapid at doing/being/bringing about x2 (event/state)

lojbo x1 reflects [Loglandic]/Lojbanic language/culture/nationality/community in aspect x2

ciska x1 inscribes/writes x2 on display/storage medium x3 with writing implement x4; x1 is a scribe

djuno x1 knows fact(s) x2 (du'u) about subject x3 by epistemology x4

nupre x1 (agent) promises/commits/assures/threatens x2 (event/state) to x3 [beneficiary/victim]

cusku x1 (agent) expresses/says x2 (sedu'u/text/lu'e concept) for audience x3 via expressive medium x4

gleki x1 is happy/gay/merry/glad/gleeful about x2 (event/state)

citka x1 eats/ingests/consumes (transitive verb) x2

plise x1 is an apple [fruit] of species/strain x2

vecnu x1 [seller] sells/vends x2 [goods/service/commodity] to buyer x3 for amount/cost/expense x4

skami x1 is a computer for purpose x2

pilno x1 uses/employs x2 [tool, apparatus, machine, agent, acting entity, material] for purpose x3

cmene x1 (quoted word(s)) is a/the name/title/tag of x2 to/used-by namer/name-user x3 (person)

bangu x1 is a/the language/dialect used by x2 to express/communicate x3 (si'o/du'u, not quote)

fanva x1 translates text/utterance x2 to language x3 from language x4 with translation result x5

mukti x1 (action/event/state) motivates/is a motive/incentive for action/event x2, per volition of x3

gasnu x1 [person/agent] is an agentive cause of event x2; x1 does/brings about x2


mi pro-sumti: me/we the speaker(s)/author(s); identified by self-vocative

do pro-sumti: you listener(s); identified by vocative

ti pro-sumti: this here; immediate demonstrative it; indicated thing/place near speaker

ta pro-sumti: that there; nearby demonstrative it; indicated thing/place near listener

zo'e pro-sumti: an elliptical/unspecified value; has some value which makes bridi true

lo veridical descriptor: the one(s) that really is(are) ...

ku elidable terminator: end description, modal, or negator sumti; often elidable

fa sumti place tag: tag 1st sumti place

fe sumti place tag: tag 2nd sumti place

fi sumti place tag: tag 3rd sumti place

fo sumti place tag: tag 4th sumti place

fu sumti place tag: tag 5th sumti place

se 2nd conversion; switch 1st/2nd places

te 3rd conversion; switch 1st/3rd places

ve 4th conversion; switch 1st/4th places

xe 5th conversion; switch 1st/5th places

xu discursive: true-false question

ma pro-sumti: sumti question (what/who/how/why/etc.); appropriately fill in sumti blank

mo pro-bridi: bridi/selbri/brivla question

na bridi contradictory negator; scope is an entire bridi; logically negates in some cmavo compounds

go'i pro-bridi: preceding bridi; in answer to a yes/no question, repeats the claim, meaning yes

su'u abstractor: generalized abstractor (how); x1 is [bridi] as a non-specific abstraction of type x2

nu abstractor: generalized event abstractor; x1 is state/process/achievement/activity of [bridi]

du'u abstractor: predication/bridi abstractor; x1 is predication [bridi] expressed in sentence x2

sedu'u compound abstractor: sentence/equation abstract; x1 is text expressing [bridi] which is x2

kei elidable terminator: end abstraction bridi (often elidable)

vau elidable: end of sumti in simple bridi; in compound bridi, separates common trailing sumti

cu elidable marker: separates selbri from preceding sumti, allows preceding terminator elision

poi restrictive relative clause; attaches subordinate bridi with identifying information to a sumti

noi non-restrictive relative clause; attaches subordinate bridi with incidental information

ke'a pro-sumti: relativized sumti (object of relative clause)

ku'o elidable terminator: end NOI relative clause; always elidable, but preferred in complex clauses

be sumti link to attach sumti (default x2) to a selbri; used in descriptions

bei separates multiple linked sumti within a selbri; used in descriptions

be'o elidable terminator: end linked sumti in specified description

pi'o pilno modal, 1st place used by ...

mu'i mukti modal, 1st place because of motive ...

gau gasnu modal, 1st place agent/actor case tag with active agent ...

pu time tense relation/direction: did [selbri]; before/prior to [sumti]; default past tense

ca time tense relation/direction: is [selbri]; during/simultaneous with [sumti]; present tense

ba time tense relation/direction: will [selbri]; after [sumti]; default future tense

zo quote next word only; quotes a single Lojban word (not a cmavo compound or tanru)

lu start grammatical quotation; quoted text should be grammatical on its own

li'u elidable terminator: end grammatical quotation; seldom elidable except at end of text

ne non-restrictive relative phrase marker: which incidentally is associated with ...

pe restrictive relative phrase marker: which is associated with ...; loosest associative/possessive

po restrictive relative phrase marker: which is specific to ...; normal possessive physical/legal

po'e restrictive relative phrase marker: which belongs to ... ; inalienable possession

.a logical connective: sumti afterthought or

.e logical connective: sumti afterthought and

.o logical connective: sumti afterthought biconditional/iff/if-and-only-if

.u logical connective: sumti afterthought whether-or-not


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