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== The Difference between Defining Equations and Constraining Equations ==
So far, the arguments of verbs have all been determiner phrases (= DPs) like names, pronouns, or Det-N (''the cat'') configurations. But verbs can also take complements of other parts of speech. This week, we will encounter a new case: namely, complements which are prepositional phrases (= PPs).


There are several types of equations that can be used in annotations. So far, we have encountered the following two:
== Prepositional Phrases ==


(1) ↑=↓1; <br>
We want our grammar to generate sentences like the following:
(2) (↑ OBJ) =↓2;


These equations are both defining equations.  
(1) The cat sat under the table.<br>
(2) Robin put food on the table.


  '''Defining equations''' add their information to an f-structure.
To achieve this, we need
   
# lexical items for the new verbs
# a phrase structure rule that creates PPs from a P and a DP
# two new phrase structure rules for verb phrases.


There is a second kind of equation, which we have not seen yet, but which you will need for the following exercise. These are called constraininig equations.
=== The Syntax of PPs ===


'''Constraininig equations''' test whether their information is contained in an f-structure. They do NOT add the information themselves.
We make the following assumptions about the internal and external syntax of PPs:


Illustration:
A. The internal structure of the PP


Case 1:
a. the P is the head of the PP<br>
b. the DP daughter of the PP bears the grammatical function OBJ


Imagine you have the following defining equation:
B. The external relationships of the PP


(↑ TENSE) = pres;
a. '''c-structure''': the whole PP is treated as just another daughter of the verb phrase whose head is the verb selecting the PP. Thus, in (1), the VP has two daughters, a V and a PP. In (2), the VP has three daughters, a V, a DP, and a PP.<br>
b. '''grammatical function''': we will only deal with PPs that express locations, for example ''under the table'' and ''on the table''. Accordingly, the verbs taking the PP as argument assign it the grammatical function '''LOC'''.


* it turns the f-structure [] into the f-structure [TENSE pres], i.e. it adds its information to the f-structure.
=== The Semantics of PPs expressing locations ===
* it turns the f-structure [TENSE pres] into the f-structure [TENSE pres], i.e. it adds its information to the f-structure. If the information was already there, the f-structure remains the same.


Case 2:
We make the following assumptions about the meaning of locational PPs like ''under the table'':


Now, imagine you have the following constraining equation:
a. the meaning of the DP ''the table'' is a LANDMARK (= orientation point).<br>
b. different prepositions take the landmark as a basis and make different locations, depending on the meaning of the preposition. Thus, ''under'' uses the landmark '''the table''' to create the location '''under the table''', whereas ''on'' makes the location '''on the table''' from the same landmark.<br>
c. sentence (1) then says that the cat is sitting in the location '''under the table''' and sentence (2) says that Robin put the food into the location '''on the table'''.<br>
d. in accordance with this, the whole PP bears the thematic role LOCATION to the verb, and<br>
e. the DP object of the preposition bears the thematic role of LANDMARK to the preposition.


(↑ TENSE) =<sub>c</sub> pres
'''Important note''': the Wiki page currently does not allow me to upload pictures. Therefore, I have uploaded '''to Olat''' the file
Exercise-8-expected-output.pdf
which gives you the f-structure and the Argument Structure that your grammar should produce for sentences (1) and (2).


* it marks the f-structure [] as ill-formed, since it does not contain the information TENSE pres, i.e. the constraining equation is a test on an f-structure.
<span style="color: blue>Exercise 8</span>
* it marks the f-structure [TENSE pres] as well-formed, but does not change it.


When to use a constraining equation:
1. Open Grammar-8<br>
 
2. Implement the analysis for sentences (1)-(2) as described above.<br>
'''Constraining equations''' are used when one item depends on some other item's adding a particular piece of information to an f-structure.
3. Parse.
 
=== The Syntax of Constraining equations in xlfg ===
 
Since xlfg does not use subscripts, it uses "==" as constraining equations.
 
Illustration:
 
'''<span style="color: red>(↑ TENSE) =<sub>c</sub> pres</span>''' becomes '''<span style="color: blue>(↑ TENSE) == pres;</span>''' in xlfg.
 
== Complement Clauses ==
 
<span style="color: blue>Exercise 8.1 (based on section 5.1 of the textbook)</span>
 
* Go to <span class="newwin">[https://xlfg.labri.fr/ https://xlfg.labri.fr/]</span>.
* Open your latest grammar.
* Add the words in the following sentences:
 
(1) Oscar thinks Sarah likes musicals<br>
(2) Oscar thinks that Sarah likes musicals
 
* Make any further changes that are necessary to obtain exactly the f-structure (10) on p. 101 for (1)-(2).
* Extend your grammar to predict the following facts:
 
(3) Oscar enquires whether Sarah likes musicals<br>
(4) *Oscar enquires Sarah likes musicals<br>
(5) *Oscar enquires that Sarah likes musicals
 
For sentence (3), you should obtain an f-structure which is identical to that of sentence (1), with the exception that the CLTYPE of (3) should be INTER.
 
Now make sure that your grammar does not license the following example:
 
(6) *Oscar thinks whether Sarah likes musicals
 
This requires the use of a constraining equation in one place!
 
'''Note:''' the solution to this exercise is going to be posted under the name ''Practical Grammar 6_solution''.
 
<!--
 
== Collecting everything we have done so far in one grammar ==
 
<span style="color: blue>Exercise 8.2</span>
 
* Go to <span class="newwin">[https://xlfg.labri.fr/ https://xlfg.labri.fr/]</span>.
* Open the grammar ''Practical Grammar 7''. Except for test sentences, it is empty.
* Open xlfg again in a second browser tab by clicking on <span class="newwin">[https://xlfg.labri.fr/ https://xlfg.labri.fr/]</span>.
* Open your previous grammars in the second tab window and copy information from those grammars into ''Practical Grammar 7'' in the first browser tab until the grammar returns the expected result for all test sentences.
 
-->
 
== Homework ==
 
<span style="color: blue>For next week, read pages 102-113 in the textbook.</span>
 
 
<br>
<br>
<br>


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<div align="center">
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Latest revision as of 06:35, 25 July 2025

So far, the arguments of verbs have all been determiner phrases (= DPs) like names, pronouns, or Det-N (the cat) configurations. But verbs can also take complements of other parts of speech. This week, we will encounter a new case: namely, complements which are prepositional phrases (= PPs).

Prepositional Phrases

We want our grammar to generate sentences like the following:

(1) The cat sat under the table.
(2) Robin put food on the table.

To achieve this, we need

  1. lexical items for the new verbs
  2. a phrase structure rule that creates PPs from a P and a DP
  3. two new phrase structure rules for verb phrases.

The Syntax of PPs

We make the following assumptions about the internal and external syntax of PPs:

A. The internal structure of the PP

a. the P is the head of the PP
b. the DP daughter of the PP bears the grammatical function OBJ

B. The external relationships of the PP

a. c-structure: the whole PP is treated as just another daughter of the verb phrase whose head is the verb selecting the PP. Thus, in (1), the VP has two daughters, a V and a PP. In (2), the VP has three daughters, a V, a DP, and a PP.
b. grammatical function: we will only deal with PPs that express locations, for example under the table and on the table. Accordingly, the verbs taking the PP as argument assign it the grammatical function LOC.

The Semantics of PPs expressing locations

We make the following assumptions about the meaning of locational PPs like under the table:

a. the meaning of the DP the table is a LANDMARK (= orientation point).
b. different prepositions take the landmark as a basis and make different locations, depending on the meaning of the preposition. Thus, under uses the landmark the table to create the location under the table, whereas on makes the location on the table from the same landmark.
c. sentence (1) then says that the cat is sitting in the location under the table and sentence (2) says that Robin put the food into the location on the table.
d. in accordance with this, the whole PP bears the thematic role LOCATION to the verb, and
e. the DP object of the preposition bears the thematic role of LANDMARK to the preposition.

Important note: the Wiki page currently does not allow me to upload pictures. Therefore, I have uploaded to Olat the file 

Exercise-8-expected-output.pdf

which gives you the f-structure and the Argument Structure that your grammar should produce for sentences (1) and (2).

Exercise 8

1. Open Grammar-8
2. Implement the analysis for sentences (1)-(2) as described above.
3. Parse.

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