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:
- I like milk in my coffee.
- 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:
|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.
- 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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