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hi friends. i have an exam on wednesday and some questions of exam are here.
i must learn the answers of these questions.

i am waiting your's help

thanks.

---Montague Grammer---

question 1:

Which of the following designate a legitimate type according to the type system which our language Ltype rests on?

a. <, <, t>>
b. <<, t>, >
c. <, , t>
d. < t, <, t>>
e. <, >

question 2:

“The dog chased John.”

Derive the semantic value of the determiner the as a higher-order expression from the translation of the sentence above abstracting away the semantic contributions of the other expressions constituting the sentence step by step.

question 3:

Suppose the following rules were added to the syntax of L1E:

VP -> Vs S
Vs -> believes-that, hopes-that

What type of semantic value would be appropriate in an extensional framework for verbs belonging to the lexical category Vs? What difficulty arises in attempting to formulate the semantic rule for Vs + S constructions?

(

Instead of recursive definitions, let us use a (context-free) phrase-structure grammar of the sort linguists are accustomed to in order to specify the syntax of L1E

Syntax of L1E

N -> Sadie
N -> Liz
N -> Hank

Vi -> snores
Vi -> sleeps
Vi -> is-boring

Vt -> loves
Vt -> hates
Vt -> is-boring

Conj -> and
Conj -> or

Neg -> it-is-not-the-case-that

S -> S Conj S
S -> Neg S
S -> N VP

VP -> Vi
VP -> Vt N
)

1 2 3 4 5
Comments  
Hello muratsekerci, and welcome to EnglishForum.
Question 1: Which of the following designate a legitimate type according to the type system which our language Ltype rests on?

I'm not sure what means here, because these logical types are a bit unusual. But as far as I know:

a. <, <, t>> ... a function from type to type <, t>. That is, a function from [one-place first-order predicates] to [second-order predicates].

b. <<, t>, > ... a function from type <, t> to type . That is, a function from [second-order predicates] to [one-place first-order predicates].

c. <, , t> ... meaningless as it stands

d. < t, <, t>> ... a function from type t to type <, t>. That is, a function from [truth values] to [second-order predicates].

e. <, > ... meaningless as it stands
Questin 2: “The dog chased John.”
Derive the semantic value of the determiner the as a higher-order expression from the translation of the sentence above abstracting away the semantic contributions of the other expressions constituting the sentence step by step.

Before answering your question I'd like to ask you: in what kind of logical language? Intensional?
Question 3: Suppose the following rules were added to the syntax of L1E:
VP -> Vs S
Vs -> believes-that, hopes-that
What type of semantic value would be appropriate in an extensional framework for verbs belonging to the lexical category Vs? What difficulty arises in attempting to formulate the semantic rule for Vs + S constructions


First of all they are not syntactic rule, aren't they?
In Montague Grammar (which is not extensional framework, but the basics are the same) these expressions like are considered: <,>. If you want a semantic value in an extensional framework, > would be appropriate, I think.

And as to the difficulty, does your teacher demand some concrete answer? There're a lot of problems (for me at least).

We still have time until Wednesday. We are waiting your post. Please explain your question more in detail.
Thank You very much Roro,

At first i want to say that i am living in Turkey,
i have learned English here.
So there may be lots of mistakes in my sentence.
i am attending to Master Licence in Computer Engineering in Trakya University.

i have studied Montauge Grammer for 2-3 months. but i don't think that i understand it.
this is not about my thesis subject. i am working on handwritten character recognition.

----------------- * -------------------

Question 2:

"Before answering your question I'd like to ask you: in what kind of logical language? Intensional?"

i am not sure. maybe in Predicate Logic or Higher-Order Type-Theoretic Language, but if it's not appropriate, then Intensional.

----------------- * -------------------

Question 2:

And as to the difficulty, does your teacher demand some concrete answer? There're a lot of problems (for me at least).

Yes. it will be pleasure with some concrete answer...

thank you again for your helping again...

Try out our live chat room.
Hello, muratsekerci !

As to your Question 2, I wrote some answer in another thread today --- because there was just the same question as your's --- so please take a look at that post: in the thread , page3.
It's in this same Linguistic section.

If my answer there won't satisfy your teacher, tell me about it! (But that's the only answer I'm aware of ...)

And as to the difficilty, let me think a little bit! I'll post about it later.

Good day, muratsekerci ! Roro
Hello, muratsekerci again. I'd better rewrite my answer here, because I made a lot of mistakes.
Question 2 “The dog chased John.”

Derive the semantic value of the determiner the as a higher-order expression from the translation of the sentence above abstracting away the semantic contributions of the other expressions constituting the sentence step by step

=
Suppose:
The expression Emotion: dog belongs to the category CN. It's logical type is.
The expression [chase] belongs to the category TV. It's logical type is <>,t>>,>.
The expression [John] and [the dog] belong to the category T. It's logical type is <>,t>.

=
John and quantified terms are translated into:
John ? ?X?X(j) (NB: the mark ? here indicates an extensional operator. Please read it as superscripted.)
the dog ? ?X?x(?y(DOG(y)?x=y)? ?X(x))

==
(1) chase John ? CHASE(??X?X(j)) (NB: the marks ? and ? here indicate an intensional / extensional operator respectively. Please read them as superscripted.) (in passing: this expression belongs to a category IV, type .)
(2) The dog chase John ? ?X?x(?y(DOG(y)?x=y)? ?X(x))(?CHASE(??X?X(j)))
(3) = ?x(?y(DOG(y)?x=y) ? CHASE(x, j))

And this is the translation of the determiner :
?Y?X?x(?y(?Y(y)?x=y)? ?X(x))

Here X, Y are both variables of type >.
x and y are variables of type e.
The mark ? indicates an conjunction, and ? indicates extensional operator.

Thus my answer to your question is ...
The semantic value of determiners is:
<>,<>,t>>


muratsekerci, I'm afraid this is not the answer you're looking for. But just take a look ... how do you think ...?
It would satisfy your teacher?
thanks again Roro

i don't know will your answer satisfy my teacher,
But it satisfied meEmotion: smile) so i admired your answer.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Emotion: smilethank you, muratsekerci !!
As to the remaining question, I'll find some answer and advise you, so ... feel easy and study hard !
See you.
Hi Roro,

here is an another question and i solved like that. I am waiting your ideas about my solution....

question:

Formulate each of the arguments in A in one of the logical systems in B. For each argument, use a logical system where you can capture its validity. In cases of ambiguity, take the interpretation that makes the argument valid. Use each logical system just once.

A.

a. Necessarily, no two presidents of the U.S. look alike.
---------------------------------------------------------------
No two presidents of the U.S. ever looked alike.

b. There is no unicorn.
-----------------------------
It is possible that John is seeking a unicorn.

c. Either all the food is terrible or no one is hungry.
It is not the case that no one is hungry.
------------------------------------------------------
All the food is terrible.

d. John admires every unicorn
Every fish is a unicorn.
----------------------------------
John admires every fish.

B.

a. Propositional Logic
b. First-Order Predicate Logic
c. Modal Tensed Logic
d. Intensional Logic

***
my answer :

a) Modal Logic

Necessarily, no two presidents of the U.S. look alike.

?x?y(President(x) ? President(y) ? x?y ? ?z(President(z) ? (z=x V z=y))_
? (??LookAlike(x,y)))

-------------------------------------------------------------------------------------------------------

b) Intensional Logic

There is no unicorn

?(?P[?x[Unicorn(x) ? P(x)]))

It is possible that John is seeking a unicorn.

?(ˆ ?x(Unicorn(x) ? Seek(john,x))

---------------------------------------------------------------------------------------------------

c. Propositional Logic

Either all the food is terrible or no one is hungry.
It is not the case that no one is hungry.
---------------------------
All the food is terrible.

A : all the food is terrible
B : no one is hungry

A V B
? B
-------
A

------------------------------------------------------------------------------------------------------

d. First-Order Predicate Logic

John admires every unicorn
?x(Unicorn(x) ? Admire(john,x))

Every fish is a unicorn.
?x(fish(x) ? Unicorn(x))

---------------------------------

John admires every fish.
?x(fish(x) ? Admire (john, x))

Hi muratsekerci !
How about d) ?
Your answers look very good, on the face of it. I'll check them more carefully later, ... because I have something to do at the moment. (would you wait till then?)
See you later!
Roro
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