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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
)

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Comments  (Page 3) 
Hello LanguageLover, and thank you for your kind words.
I've read before your posts for several times. They gave me very good impression. I've never thought that English is your second language.

I'm not a linguist yet ... so I will learn a lot from you! Thank you.
And you are so down to earth. I like that. I started a thread with the subject "Hi Roro" in the same linguistic section.
Cheers,
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Hello muratsekerci, and sorry for my slow reply. It's not that I forgot your question, ... simply ... I'm not a specialist at all yet in formal semantics, and I'm in the course of thought, to which I'm accustomed.
I'd like to answer to your question, one by one, if you're not in a hurry.
See you. Roro
Hello muratsekerci.

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

Your 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)))



muratsekerci, I'm sorry, I don't know the translation of . I've learned only or . When you know the answer, please kindly tell me the answer!

As to the solution, we maybe need not to translate this proposition, I think. Simply put the proposition as f, and
? f ? f


I think this captures the validity of argument.
I'm not so sure: I ignored temporal factor here, although there is in the choices an item .

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

Your Answer: 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))


Hi muratsekerci. Your choice is right, but there're minor mistakes. I think ...

There is no unicorn = ?(?P[?x[Unicorn(x) ? P(x)]]) ... this is not a proper translation.

It would be better: ??x[Unicorn(x) ? ?P(x)]
(NB: this ? is an extensional operator)

And the sentence is an ambiguous sentence. It has two readings: de dicto & de re reading. Here we should consider the de dicto one, I suppose, thus:
? (***(j, ˆ?P?x(Unicorn(x) ? ?P(x)))

------------------------------- thus ------------------------------------------------------------
??x[Unicorn(x) ? ?P(x)]
? (***(j, ˆ?P?x(Unicorn(x) ? ?P(x)))
---------------------------------------------------------------------------------------------------
If I made a mistake, please kindly tell me about it. I will appreciate that.
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c) is correct.
I think d) is correct, too.
Hello muratsekerci. Can I ask you a question?
There are something that I cannot understand yet. In your first post, you added ... or edited:
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 etc.etc.


How and why?
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Hello
Could anybody explain it please ... ?
I really need some explanation.
Why did they .. and other parts .. appear right in front of my eyes?
When I was writing my answer to muratsekerci?
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