A conjunction is a particle that combines two constituents (grammatical units) into one.
For example, ru “and”, ra “either/or”, and roı “together with” are all conjunctions.
A logical conjunction is one that expands to some logical operation on the truth values you get when committing to either conjugand and parsing the rest of the clause.
For example, X ru Y is a logical conjunction, corresponding to a logical “AND” operation on the “X sentence” and the “Y sentence”: Bỏ jí ru nháo sa pỉano is interpreted as (Bỏ jí sa pỉano) & (Bỏ nháo sa pỉano).
The logical conjunctions are: ru “and”, ra “either/or”, ro “xor”, and rı “which one?”.
They can combine noun forms, verb forms, adverbials, prepositions, relative clauses, and statements: see the refgram.
On combining verb forms
Logical conjunctions of verb forms have “combine the sentences” semantics inside their would-be definition, rather than causing a bifurcation in the clause they're in.
For example, bảo ru kủo is a new verb form meaning “___ is white, and it is black”.
So Nẻo sa bảo ru kủo tóq claims that there is a black-and-white thing on the table. We do not read it as (Nẻo sa bảo tóq) & (Nẻo sa kủo tóq). If this meaning is desired it can be recovered by combining noun forms instead: Nẻo sa bảo ru sa kủo tóq.
On combining statements
To say “I work and you rest”, you might try Gủaı jí ru sẻa súq. But this is incorrect: jí ru sẻa is a noun form meaning “that which is me and rests”. (It's the tone-conjugation of the conjoined verb form jỉ ru sẻa.)
Statements are correctly combined by placing the statement-terminator particle na in front of the conjunction.
This particle used to see more uses that have been superseded by cy and ky, and now this is its only function.
Gủaı jí na ru sẻa súq da.
I work and you rest.
On adverbial scope
🚧 Does Jỏe bũ jí ru súq have a different meaning from Jỏe jí ru súq bũ? Mỉ mỉu says so:
Jỏe bũ jí ru súq.
It's not true that [I'm skilled and you're skilled].
Jỏe jí ru súq bũ.
I'm not skilled, and you're not skilled.
A non-logical conjunction is one that combines two noun forms into a new noun form, without such “logical expansion” semantics.
The only non-logical conjunction in standard Toaq is roı “together with”, which takes the plural logic “sum” of its conjugands.
Hỉe súq roı jí sa shỉ cẻa da.
You and I (together) carry a bag.
Hỉe súq ru jí sa shỉ cẻa da.
You carry a bag, and I carry a bag.
Joining things that aren't noun forms with roı is a bit semantically dubious. Possibly, joining statements with roı means something like claiming a “sum event” of two things happening together, maybe in the same time/place/context, rather than claiming that one happens and the other happens.
Instead of “X conjunction Y”, you can say “to conjunction X to Y”, which has the conjunction in front of both arguments, yielding a structure similar to “either X or Y” or “both X and Y” in English.
Infix conjunctions, perhaps surprisingly to Lojbanists, associate (i.e. group) rightwards.
nủı ru lủe ra bảo ro dẻ
small AND (yellow OR (white XOR pretty))
You can use to as "parentheses".
to ra nủı ru lủe to bảo ro dẻ
(small AND yellow) OR (white XOR pretty))