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J connects prepositions to their objects.

             +-Mp+----J---+    +-----MVp----+-J-+
             |   |        |    |            |   |
        The man with the hat chased the dog on Tuesday
Proper 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".

Js, Jp, Ju: Singular, plural, uncountable

The Js, Jp and Ju forms are as described above, with the subscripts indicating singular, plural or uncountable (mass noun) attachements.

Jw: Questions

Jw is used to connect prepositions to noun-phrase question-words in the construction "To whom were you speaking?" The construction formed here is very similar to that formed for determiner-question-words, as in "To which person were you speaking?" See "JQ" for an explanation. Jw is also used in prepositional relative clauses, like "The room IN WHICH I was working was cold". See "Mj".

Jr, Jm, Jy: Relative and comparative clauses

Regarding Jr, see "B: Noun-Modifying Prepositional-Object Relative Clauses". Jm and Jy relate to comparatives; see "MV: Comparatives", sections II (Jm) and VII (Jy).

Jd: Determiners

Jd is used with quantifying or quasi-numeric determiners. The resulting linkage forms a loop, together with the D link, thus:
               |         +----Dmc----+
               |   +--Ds-+-OFd-+--Jd-+
               |   |     |     |     |
          I have.v a number.d of cookies.n 
In 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.

Jj, Jk: Link-crossing over conjunctions

Jj and Jk are used together to violate the graph-planarity rule, so as to build a fractured link that crosses over a conjunction:
          |     +--VJlpi--+-----------Jk----------+
          |     +-MVp+-Jj-+--VJrpi-+--MVp-+---Js--+
          |     |    |    |        |      |       |
   ...  to.r look.v at and.j-v listen.v to.r everything
Here, the Jj and Jk should be taken as artificially forming a single link, that crosses over the conjunction, and indicates that the prepositional object of "at" is "everything". (Paraphrasing, "... to look at everything and listen to everything.") In this example, there is no way to create a single Js link from "at" to "everything" without voilating planarity. Thus, planarity is maintained by splitting Js into two, with the split being a "hole" or "jump", allowing limited non-planarity. Thus, Jj and Jk can be thought of as forming a single link, with a "hole" in it, with that hole being exactly the right shape to hop over the conjunction.

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