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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 2) 
Hello muratsekerci !
Question 3: Suppose the following rules were added to the syntax of L1E:

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

What difficulty arises in attempting to formulate the semantic rule for Vs + S constructions?

I think there could be various technical problems. And there are at least two big semantic problems, which we cannot treat in a first-order predicate logic.

[1] Problem of opaque context, & [2] Problem of tense / tense-aspect.


[1] believe (that..), hope (that..) : these kind of words give rise to a so-called opaque context (Quine's term), in which the principle of extentionality is no longer valid.

(In passing: a logical system is said to be extensional if expression with the same reference may be freely substituted for each other. And a first-order predicate logic is extensional.)

(1) The president of the United States of America is the supreme commander of the U.S. armed forces.

This sentence says: two definite descriptions have the same reference. Thus in extensional logical language we can substitute one expression for the other.

------------------------------------------------------------------------------------------
But in a opaque context we cannot.

(2) John believes that his neighbour is the president of the United States of America.

(3) John believes that his neighbour is the supreme commander of the U.S. armed forces.

(2) and (3) could have different truth values. (In order to solve this problem we need to expand logical system. We need some intensional logic.)


[2] Problem of tense / tense-aspect.
This is a big problem of a first-order predicate logic, too, but I think ... [1] would be a better answer. I'd better not to expand on this.


Thus my answer to your qestion is: these kind of verbs give rise to a so-called opaque context (Quine's term), in which the principle of extentionality is no longer valid.
Hello muratsekerci !

As to the other exercises, , I haven't met these kind of exercises until now. Looks interesting, and your answers show your competence.
Are you in a hurry? Can I answer a bit later?
So long!
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Sorry guys for the interruption. When I first had a look at the thread, I wondered if you've studied linguistics! (Since I have a linguistics degree and we didn't have such assignments!) Then, Muratsekerci has cleared up my doubts about his major, and I was a bit relieved! What about you Roro, if you don't mind the question?
Hello LanguageLover, I'm very glad to meet you. First of all I like your handle name.
Yes, this is a relatively new trend in Lingustics (Formal Semantics wasn't in my assingments, too. I learned it myself). New, but becoming influential more and more. (It's for sure!)

In those days when I began to learn it, I felt dizzy, got giddy every time when I got a glimpse of these logical formulae. Then I realized: it's because they contain in themselves far more information than usual terms.

I'm looking forward to talking with you about lingusitics et alia in this forum. Roro
Thanks Roro and thanks LanguageLover..

Roro your wonderful answers expands my knowledge and imagination.

i liked this consultation and i want to continue (if you want),

LanguageLover, we will be glad if you tell your ideas about solutions.

and new questions and my answers: (i am waiting your interpretations...)

Question 1: Translate the following sentence into predicate logic in a way that captures the constraint that there is a unique dog in the universe of individuals:

“The dog chased John.”

Answer:

?P?x(?y(DOG(y)?x=y)? P(x))?CHASE(x,John)

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

Question 2 Emotion: big smileo a complete syntactic and semantic derivation (i.e. translation) of the sentence “John believes that a man or a woman walks” that will give “a man” a 'de dicto' reading while “a woman” receives a 'de re' reading

Answer :

Believe(John, ˆ?x(Man(x) ? Walk(x))) V ?y(Woman(y) ? Believe(John, ˆ(walk(y)))

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

Question 3:

We have suggested that no distinction should be made between subjects and objects when truth-conditionally evaluating sentences. Consider, however, pairs of sentences like the following:

(a) The King of France is bald.
(b) I saw the King of France in an exhibition yesterday.

While "b" could be straightforwardly evaluated as false, whether the same would be so easily said about "a" is controversial. "a" could be treated either as false or undefined. Briefly discuss the issue in terms of the subject-object asymmetry/symmetry and two-valued logic

Answer :
if the king of friend is not a member of the set of bald then we can say "a" is false.

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

Question 4:

Discuss the Russellian way of avoiding paradoxes (i.e. via a system types) in terms of its applicability to natural language.

Answer :

i have't got a good idea..
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Hello muratsekerci. Just my first impression .. I'll answer later.

[Question1] “The dog chased John.” = ?P?x(?y(DOG(y)?x=y)? P(x))?CHASE(x,John)

... no. This is not a proper translation. ?Pf ... this expression is not an expression of type t.

[Question2] The most important thing is how to derive this translation compositionally, I think.
And I'm afraid I don't know the answer. It's beyoud my knowledge.

[Question3] It seems to me that this question concern the debate made between Russell and Strawson. And actually I don't know .... whether the subject-object asymmetry/symmetry matters here.

[Question4] I think it's quite easy: we just made a decision and introduce a rule to avoid paradoxes.
(Sorry ... I'll try to explain the way that Russell took later.)

See you.
Thanks Roro,
I'll open up a new thread for talking to you. This way, I won't interrupt anything!
Hello LanguageLover, ... your interrution was pleasant for both of us ... and it wasn't any interrution at all in the first place.
I'm not good at English, but I'm looking forward to talking with you. Roro
Students: We have free audio pronunciation exercises.
You're very kind Roro. English is also my second language, and I make lots of mistakes myself. Don't worry about that. I'm searching for something, I'll be with you in a couple of minutes! Thanks
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