Help Please!

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>> ... 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.

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

thanks again Roro

i don't know will your answer satisfy my teacher,
But it satisfied me) so i admired your answer.

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

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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)))

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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))

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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

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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))