I've been learning Greenlandic and I came across this term, and I can't find anything about it online. Can anyone explain it in Layman's terms?
I know this is an old post so you might not need an answer anymore, but I thought I'd give one since I encountered this same terminological problem when I was doing research on "non-Bakerian" patterns of noun incorporation a few years back. I believe this term is idiosyncratic to Michael Fortescue's 1984 grammar of Kalaallisut; he might have borrowed it from other writers on Yupik-Inuit languages, I'm not sure. In any case, it's not a term used by linguists outside of the grammatical description of Yupik-Inuit languages.
What he's describing with "half-transitivity" is antipassivity. This is when a lexically transitive verb (which ordinarily takes transitive morphology + an accusative- or absolutive-marked internal argument) appears in a configuration with intransitive morphology and with the internal argument marked in an oblique case. In other words, it's a construction where a lexically transitive verb is realized in such a way that it is grammatically, syntactically, and morphologically intransitive. English doesn't use the antipassive voice productively, but there's a few quaint examples. The cow is chewing cud means nearly the same thing as The cow is chewing on cud, but syntactically, the sentence without on is transitive and takes a direct object, while the sentence with on is intransitive and takes no direct object (the internal argument is instead realized as a prepositional phrase, on cud). Kalaallisut does this all the time, and it's a fully productive pattern. In a lot of languages (including the Inuit languages), the antipassive voice indicates that the internal argument is "less specific" than its correspondent in the active voice.
To use an example from Inuktitut:
ilisaji niuviq-tuq saa-mik uujaujar-mik
teacher.ABS.SG. buy-3SG.SUBJ. table-OBL.SG. which.is.green.-OBL.SG.
"The teacher bought a green table."
The subject (ilisaji) is absolutive; the verb (niuviqtuq) is morphologically intransitive; and the internal argument (saamik uujaujarmik) is marked in the oblique case. Semantically, it has a transitive meaning, but grammatically, it's intransitive. Fortescue would call this a "half-transitive" construction, but to most linguists, it's called an antipassive construction.
Compare this to its active voice counterpart:
ilisaji-p niuviq-taa saa uujaujaq
teacher-ERG.SG. buy-3SG.SUBJ.3SG.OBJ. table.ABS.SG. which.is.green.ABS.SG.
"The teacher bought the green table." (notice the, instead of a)
The subject (ilisajip) is ergative; the verb (niuviqtaa) is morphologically transitive; and the internal argument (saa uujaujaq) is absolutive. Grammatically and semantically, this sentence is transitive, and it's in the active voice.
I hope this very, very late answer helped! (I've only used this site a few times so I don't know if answering old questions is allowed, please forgive me if not.)