How do relative pronouns (which, who, invisible which= WH) fit into a sentences compositionality? Given that relative clauses modify Noun Phrases, I'd expect them to be of type <et,<et>> which fits nicely into the semantic structure. However, what of which? What is its type? The denotation of (1), under a Fregian view, would be ιx[CAR(x)∧DESTROY(t,x)] which would be the same as (2).

(1) The car which Tom destroyed.

(2) The car Tom destroyed.

Assuming the TP Tom destroyed which is <t> and the Relative Clause which Tom destroyed which is <et,<et>>, I assumed which would be of type <<t>,<et,<et>>>> but given that it's an argument of destroy it must be of type <e>. Something must be wrong in my assumption of which being <<t>,<et,<et>>>>. I'm assuming Lamda extraction would come into place to assign a variable to which so that it refers to the car but where would it come in place? And how would it work with that instead of which as that is semantically vacuous as of type <t,t>? I am confused as to how to get to the entire DP to <e>...

Any help/ nudging to the correct direction would be much appreciated. I have included a semantic derivation for (1) as a hyperlink.

  • No offence meant, but is the point in formalising phenomena which do not need it? What is the import of positing a surface structure derived from an assumed underlying one apart from some Chomskian nostalgia?
    – user27758
    Commented Apr 28, 2020 at 16:46
  • By the way, restrictive relative clauses modify nouns (or N-bars according to McCawley), not NPs.
    – Greg Lee
    Commented Apr 28, 2020 at 17:32
  • A preliminary point, if I may. Relative clauses don't modify noun phrases; they mostly modify nominals (there is a difference). And even then, it's only integrated (defining) relatives that are modifiers. The supplementary (non-defining) kind are supplements, not modifiers, though they do have full NPs as antecedent.
    – BillJ
    Commented Apr 28, 2020 at 17:33

2 Answers 2


This is a good start and your calculation works out, but the standard literature wouldn't agree on your suggestion that Tom destroyed is of type t. The crucial point is that that the moved-away pronoun makes the phrase something that's missing an entity to become a sentence with a truth value, so in accordance with your lambda abstraction, which is expecting an individual argument to produce a truth value, this relative predication Tom destroyed would be of type <e,t>. In the tree, the verb destroy does not actually pick up the value of the trace to combine to <e,t>, but will remain with the object position unsatisfied.
The motivation behind this is, I imagine, that if you moved the which to a different position, you can't just squeeze out its semantic content twice and use it simulateneously as a relative pronoun and as an object to the verb phrase. It's one syntactic object that can only contribute to the meaning of the sentence once. So in the type decomposition, since the element indexed by i now serves its purpose as the specifier of the TP and can thus no longer contribute any semantic content to the completion of the VP in object position, it will be treated semantically as if it wasn't there in its original node. (Though we know that syntactically, the position will remain occupied with the trace blocking any other syntactic elements from filling the slot.)

Let's break it down step by step:

In the following (alternative see below), I will follow your suggestion that syntactically, car is an NP which first combines with the CP which Tom destroyed to another NP, to which afterwards the determiner the is applied to produce a DP:

  [D [the]]
    [NP [car]]
    [CP [which Tom destroyed]] ]

As you correctly figured out, relative clauses act as predicate modifiers, and are thus of type <<e,t>,<e,t>>: They take an NP of type <e,t> and produce another NP <e,t>, which then combines with the determiner the to form a DP of type e:

|    the       car     which Tom destroyed |
|           | <e,t> |    <<e,t>,<e,t>>     |
| <<e,t>,e> |           <e,t>              |
|               <e>                        |

So if the (possibly phonetically empty) relative pronoun (which) is to be an operator that is applied to the relative predication (Tom destroyed) to yield the relative clause (which Tom destroyed), it should be of type <σ,<<e,t>,<e,t>>>, where σ is the type of the relative predication:

|    the       car           which        Tom destroyed |
|           |       | <σ,<<e,t>,<e,t>>> |       σ       |
|           | <e,t> |            <<e,t>,<e,t>>          |
| <<e,t>,e> |                  <e,t>                    |
|                        <e>                            |

The relative predication is something that's missing an individual (the "trace") to become a sentence with a truth value: {x: Tom destroyed x}. This is dreivable from the fact that destroyed is a two-place verb (type<e,<e,t>>) that so far has been fed one individual (Tom: type e), thus our σ is the type <e,t>:

|    the       car              which         Tom   destroyed |
|           |       |                       |  e  | <e,<e,t>> |    
|           |       | <<e,t>,<<e,t>,<e,t>>> |      <e,t>      |
|           | <e,t> |                <<e,t>,<e,t>>            |
| <<e,t>,e> |                     <e,t>                       |
|                              <e>                            |

Eventually, we get that the relative pronouns must be of type <<e,t>,<<e,t>,<e,t>>>.

There should be no difference between which, who, that, and a phonetically empty -- they all have the same type-compositional behavior. I don't follow why you assume that that should be of type <t,t> or what you men by "semantically vacuous"; you'd have to elaborate more on that.

Some may prefer an analysis where the relative clause is only attached after the NP already combined with the determiner:

     [D [the]]
     [NP [car]] ]
   [CP [which Tom destroyed]] ]

In this case, 1) for definite DPs (the car) which have type e: the relative clause must be of type <e,e> and the relative pronoun of type <<e,t>,<e,e>>; 2) for quantified DPs (a car) which have type <<e,t>,t>: the relative clause must be of type <<<e,t>,t>,<<e,t>,t>> and the relative pronoun of type <<e,t>,<<<e,t>,t>,<<e,t>,t>>:

|   the       car         which       Tom destroyed |
| <<e,t>,e> | <e,t> | <<e,t>,<e,e>> |      <e,t>    |
|         e         |             <e,e>             |
|                           e                       |

|          a            car                which               Tom destroyed |
| <<e,t>,<<e,t>,t>> | <e,t> | <<e,t>,<<<e,t>,t>,<<e,t>,t>>>> |     <e,t>     |
|          <<e,t>,t>        |              <<<e,t>,t>,<<e,t>,t>>             |
|                                  <<e,t>,t>                                 |
  • I was initially confused as several literature analysed RCs through Predicate Modification, thus being of type <et,<et>>. This analysis seemed pretty useless to me as it seemed to add exceptions to a pretty systematic and logically straight-forward system. As to your comment about quantified DPs, I've seen several literary work analysing them as either the RC modifying (1) the NP car first or modifying (2) the DP every car . What approach is considered the better approach? The only difference I can see is the matrix DP type, where in (1) it is <et,<t>> and in (2) <e>. Commented Apr 30, 2020 at 19:31

The view which emerged from Lauri Karttunen's classic paper "Migs and Pilots" is that a relative pronoun is coreferential with the NP relative clause construction it occurs in. See Pauline Jacobson. I guess that would make it type e.

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