J connects prepositions to their objects.
+-Mp+----J---+ +-----MVp----+-J-+ | | | | | | The man with the hat chased the dog on TuesdayProper and common nouns, accusative pronouns, and other words that can act as noun-phrases have "J-" disjoined with their S+, SI-, and O- connectors.
Prepositions have "J+ & (Mp- or MVp-)". "Mp" is used for prepositions modifying nouns; "MVp" is used for prepositions modifying verbs and adjectives. Prepositions may also have other connectors, disjoined with J+, such as Mg+, Mv+, and QI+; see "MV: Other Uses of MVp and MVs".
+----------Op---------+ | +----Dmc----+ | +--Ds-+-OFd-+--Jd-+ | | | | | I.p have.v a number.d of cookies.nIn the above example "a number of" is acting effectively as a determiner phrase. Thus, its head word, "number", gets a D+ link. Yet, the phrase ends with a preposition that shouldn't dangle, and so, for this case, a Jd+ link is also used to complete the loop. Plural and mass nouns have a (Jd- & D- & O-) disjunct on them.
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