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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  (Page 5) 
Hallo
I'm slightly confused. Actually, I have not the slightest idea what you guys are talking about:)

I have some linguistic background, however, i have always been interested in historical linguistics, therefore, I don't really follow your posts. You know, all these signs like:

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

I know they are logical signs, but that's all I know. Anyway I'm eager to learn something
about the things you were discussing. Was it formal semantics, Montague Grammar?

Can you recommend some 'basic' websites (or .pdf files) where i can start my journey
through montague grammar and all these things?

Thank you very much

Agent C
hi agent c

we are discussing the translations of sentences and some types of examples in montague grammer.

this is my "formal semantics" lesson in school.

i don't know well this issue but Roro helped me much.
so i increase my knowledge a bit with discussing.

this is the first handout of the lesson:
------------------------------------------------------

Introduction to Logic

Logic as the Science of Reasoning

Logic can be defined as the science of reasoning or the science of relationships between meanings. Argumentation is an important application of reasoning. The trains of reasoning studied in logic are called arguments, or argument schemata. The business of logic is to find out what it is that makes a valid argument (or a valid inference) valid.

An argument can be conveniently seen as a finite collection of declarative sentences in some language, where a single sentence is distinguished as the conclusion, and where the other sentences constitute the premises. An argument is valid iff it is not possible for the premises all to be true while the conclusion is false. In other words, if the premises were all true, then the conclusion would have to be true. So a valid argument has no possible counterexample. A sound argument is a valid argument with true premises.

Some Examples of Valid Arguments

Below are a few examples of valid arguments:

(1) John will come to the party, or Mary will come to the party.
John will not come to the party.
---------------------------------------
Mary will come to the party.

(2) John will come to the party, or Mary will come to the party.
If John has not found a baby sitter, he will not come to the party.
John has not found a baby sitter.
---------------------------------------
Mary will come to the party.

(3) All airplanes can crash.
All DC-10s are airplanes.
-------------------------------
All DC-10s can crash.

(4) John is a teacher.
John is friendly.
-------------------------------------
Not all teachers are unfriendly.

(5) All fish are mammals.
Moby *** is a fish.
------------------------------
Moby *** is a mammal.

All of these examples are valid: anyone who accepts that their premises are true will also have to accept that their conclusions are true. Take (1) for instance. Anyone can see that (1) is a valid argument without even being able to ascertain the truth or falsity of its premises.

Validity of an Argument and the Truth or Falsity of its Premises and Conclusion

Apparently one does not even need to know who Mary and John are, let alone anything about their behavior with respect to parties, in order to say that the argument in (1) is valid (i.e. in order to say that if the premises are all true, then so must its conclusion be.

That the premises of a valid argument can even be plainly false is apparent from example (5). Obviously both premises of this argument are false, but that does not stop the argument as a whole from being valid. If one were to accept that the premises were true, then one would also have to accept the conclusion.

Not only is the factual truth of the premises not necessary for argument to be valid, it is not sufficient either. This is clear from the following example:

(6) All horses are mammals.
All horses are vertebrates.
-----------------------------------
All mammals are vertebrates.

Both the premises and the conclusion of ( 6 ) are in fact true, but that does not make ( 6 ) valid. Accepting the truth of its premises does not involve accepting that of the conclusion, since it is easy to imagine situations in which all of the former are true, while the latter, as the result of a somewhat different mammalian evolution, is false.

Argument Schemata

But if it is not the truth or falsity of the premises and the conclusion of an argument which determine its validity, what is it then? Let us return to example (1). We have pointed out that we do not even have to know who John is in order to say that the argument is valid. The validity of the argument actually has nothing to do with John Personally, as can be seen if we exchange him for someone else, say Peter. If we write “Peter” instead of “John”, the argument remains valid:

(7) Peter will come to the party, or Mary will come to the party.
Peter will not come to the party.
---------------------------------------
Mary will come to the party.

The name “John” is not the only expression which can be exchanged for another while retaining the validity of the argument:

(8) Peter will come to the meeting, or Mary will come to the meeting.
Peter will not come to the meeting.
---------------------------------------
Mary will come to the meeting.

If we try out all of the alternatives, it turns out that or and not are the only expressions which cannot be exchanged for others. Thus (9) and (10), for example, are not valid arguments:

(9) John will come to the party, or Mary will come to the party.
John will come to the party.
---------------------------------------
Mary will come to the party.

(10) John will come to the party if Mary will come to the party.
John will not come to the party.
---------------------------------------
Mary will not come to the party.

From this it is apparent that the validity of (1) depends only on the fact that one of the premises consists of two sentences linked together by the conjunction or, that the other premise is a denial of the first sentence in that premise, and that the conclusion is the second sentence. And (1) is not the only argument whose validity depends on this fact. The same applies to (7) and (8), for example. We say that (1), (7), and ( 8 ) have a particular form in common, and it is this form which is responsible for their validity. This common form may be represented schematically like this:

(11) A or B
Not A
--------
B

These schematic representations of arguments are called argument schemata. The letters A and B stand for arbitrary sentences. Filling in actual sentences for them, we obtain an actual argument. Any such substitution into schema (11) results in a valid argument, which is why (11) is said to be a valid argument.

The ‘form’ we said could be represented by (11) is more than just a syntactic construction. The first premise is not just two sentences linked by a conjunction, for it is also important what conjunction we are dealing with. A different argument schema is obtained if the conjunction or in (11) is replaced by another conjunction, say, if:

(12) A if B
Not A
--------
B

This schema is not valid. One of the substitutions for A and B is, for example, (10), and that is not a valid argument. That expressions other than the conjunctions can lead to arguments being valid becomes apparent if we examine example (5) in more depth. Considerations similar to those for (1) lead to the following argument schema for (5):

(13) All P are Q
a is P
-------
a is Q

In this schema the letters P and Q stand for expressions which refer to properties, and a stands for an expression which refers to an individual or an entity, that is, to a material or an abstract object. It will be clear that every substitution for a, P, and Q results in a valid argument; (5) is one example of these. The validity of this schema derives from, among other things, the meaning of the quantifying expression all. Other examples of quantifying expressions to be found in argument schemata are some and no.

Logical Constants and Logical Systems

To sum up, logic, as the science of reasoning, investigates the validity of arguments by investigating the validity of argument schemata. Argument schemata are abstractions which remove all those elements of concrete arguments which have no bearing on their validity and keep those expressions that play a part in this issue.

In fact, there is no such thing as a universal logic which characterizes all valid arguments. In practice, different logical systems are developed, each with its own particular class of arguments. What class this is or, equivalently, what logical system we have, depends on the kinds of expressions on whose meanings the validity of arguments is based on. The expressions which play this part in a logical system are called its logical constants, since within that system their meaning is completely fixed. Below are some sets of logical constants associated with the logical system which they are treated in:

(14) LOGICAL CONSTANTS LOGICAL SYSTEMS

and, or, if (…then), if an only if, it is not the cased that----------- Propositional Logic
all, some--------------------------------------------------------------- First-Order Predicate Logic
possibly, necessarily ------------------------------------------------ Modal Logic
it was the case that, it will be the case that ----------------------- Tense Logic
believe, know, etc.--------------------------------------------------- Intensional Logic

The set of possible logical constants is an open one. We could give some more examples of expressions for which logical systems have in fact been developed, but it turns out to be extremely difficult to specify the set of all expressions for this would make sense.

We should, finally, note that enlarging our set of logical constants is not the only way new logical systems can be developed. We can also consider the same set of logical constants under a new interpretation.This too results in a different class of valid argument schemata. So besides so-called classical propositional logic we have, among other alternatives, intuitionistic propositional logic, in which the same logical constants receive a slightly different interpretation. Strictly speaking, then, a logical system is characterized by its logical constants together with the interpretations placed on them. However, the dimension of devoloping new logical systems via variations in interpretation will remain outside the scope of this course.
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Hello muratsekerci
I see. Sorry.
I just wanted to know how to edit.
After you sent your post.

Because I saw twice, in front of my eyes, while I was writing my answer, in another window, your texts were edited.

(For example, in my post, 9th in page 1, I wrote:

Hi muratsekerci !
How about d) ?
(Posted: 06-10-2005 04:58 AM)

Then just one minute ago, in the previous post, your answer d) was added, in another window.

This is why I asked you: .

Please tell me how, because it would be very convenient for me, if you don't mind , when you have spare time.

Thank you.

Nice to meet you, Agent C.

I'm interested historical linguistics a little bit, too. It's most intriguing & exciting field in linguistic research, maybe.

As to the introduction, muratsekerci's description is from L.T.F. Gamut, vol.1., and this is the best introduction, but not so handy.

(In passing: there is one place in which the authors made a sloppy mistake in this quote.
Description about (10) and (12) should be revised, I think. There's a mistake.)

If you are interested in these formal headaches, I'd explain them in general, with pleasure.
At least I'm trying to explain them in some another threads.

Very nice talking to you, Agent C.
Hello muratsekerci
I have changed my mind. Actually I'm not so interested in the way how you managed to add your answer to your previous posts. I can do without it. I'd like to giving up discussing.

By the way there's a mistake in your quote, I think, as I mentioned in my previous post to Agent C.

Hope you would pass the exam. There's no need for your answer.
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Hi Roro

my exam was very good.
i think i will pass the exam..

thank you very much for your helphing.

here is a article which my teacher gave us.
it is about mankind.

this article is a part of a Risale-i Nur Collection.
whole of Risale-i Collection is consist of 6000 page and it is translated about 40 languages.
there are millions of readers of Risale-i Nur in the world.

maybe it will be interesting for you...

FIRST REMARK

Man stands in need of most of the varieties of beings in the universe and is connected to them. His needs spread through every part of the world, and his desires extend to eternity. Just as he wants a flower, so too he wants the spring. Just as he desires a garden, so does he also desire everlasting Paradise. Just as he longs to see a friend, so does he long to see the All-Beauteous One of Glory. Just as in order to visit one he loves who lives in another place, he is in need for his beloved's door to be opened to him, so too in order to visit the ninety-nine per cent of his friends who have travelled to the intermediate realm and so be saved from eternal separation, he needs to seek refuge at the court of an Absolutely Powerful One Who will close the door of this huge world and open the door of the hereafter, which is an exhibition of wonders, and remove this world and establish the hereafter in its place.Thus for man in this position the only True Object of Worship will be One in Whose hand are the reins of all things, with Whom are the treasuries of all things, Who sees all things, and is present everywhere, who is beyond space, exempt from impotence, free of fault, and far above all defect; an All-Powerful One of Glory, an All-Compassionate One of Beauty, an All-Wise One of Perfection.

And so, O man, if you are the slave of Him alone, you will earn a place superior to all creatures. But if you hold back from this servitude to Him, you will become an abased slave to impotent creatures. If you rely on your ego and own power and abandoning reliance on God and supplication, deviate into pride and boasting, then you will fall lower than an ant or bee in regard to goodness and creation, and become weaker than a spider or a fly. You will become heavier than a mountain in regard to evil and destruction, and more harmful than a pestilence.

Yes, O man! You have two aspects: one is that of creation, good, acts, and positivity. The other is the aspect of destruction, non-existence, evil, negativity, and passivity. In regard to the first aspect, you are lower than a bee or sparrow, and weaker than a spider or fly. Whereas in regard to the second aspect, you surpass the mountains, earth, and skies; you take on a burden before which they expressed their impotence and from which they shrank, and you assume a sphere more extensive and vaster than them. For when you create and do good, you are able to do so only to the extent of your own power and strength and to the degree your hand can reach. But when you commit evil and destruction, then your evil overwhelms and your destruction spreads.

For example, unbelief is an evil, a destruction, an absence of affirmation. But that single evil comprises insulting the whole universe, belittling all the Divine Names, and abusing all humanity. For these beings have elevated positions and important duties; they are Dominical missives, Divine mirrors, and Divine officials. But unbelief dismisses them from their rank of being mirrors, officials changed with duties, and bearing meanings, and reduces them to the level of futility and being the play-things of chance. And through the destruction of death and separation, it lowers them to the degree of being swiftly decaying ephemeral matter lacking all importance and value, to being nothing. And so too through denial it insults the Divine Names, the inscriptions, manifestations, and beauties of which are to be seen throughout the universe and in the mirrors of beings. And it casts down to a position more abased and weaker, more powerless and needy than the lowliest transient animal the one who holds the rank of God's vicegerent on earth, known as man, who is a well-composed ode of wisdom proclaiming the manifestations of the Sacred Divine Names, and a seed-like self-evident miracle of Divine Power containing all the members of an eternal tree, and who, with assuming the 'Greatest Trust', became higher than the earth, sky and mountains and gained superiority over the angels. It reduces him to the level of being a common sign-board lacking all meaning, confused, and swiftly decaying.

In Short: In regard to destruction and evil, the evil-commanding soul may commit infinite crimes, but concerning creativity and good, its power is extremely little and partial. Yes, a house may be destroyed in one day, while it cannot be built in a hundred. However, if the soul gives up egoism and seeks good and existence from Divine assistance, and if it foregoes evil and destruction and relying on the soul, and seeking forgiveness becomes a true slave of God's, then it will manifest the meaning of the verse,God will change their evil into good.

Its infinite capacity for evil will be transformed into an infinite capacity for good. It will acquire the value of the Most Excellent of Patterns and ascend to the highest of the high.

And so, O heedless man! Look at Almighty God's munificence and generosity! Although it would be justice to record one evil as a thousand and a single good deed as one or not at all, He records a single evil as one, and a single good deed as ten, and sometimes as seventy or seven hundred, or even sometimes as seven thousand. You will also understand from this Remark that to be sent to Hell, which is so dreadful, is retribution for the deed and pure justice, while to be sent to Paradise is pure generosity.

and a diffrenet part in japanese...
(execuse me if there are mistakes because of the japan fonts)

<removed by mod; please write in English only>
Thank you guys for your explanation:)

Since it's quite new for me, I need a few days to mull it over before I will have any comments

As far as historical linguistics is concerned, I have spent a lot of time on the language of
Shakespeare, notably its verbal group.

Agent C
Hello Muratsekerci and Roro

Thanks for Gamut's introduction. I've read it and so far It's been pretty straightforward:)
Can we go a step further? Thank you

By the way, I think I recognised the mistake in (10) and (12)
A is dependent upon B, not the other way round. Hence it is mistaken to claim that if John will not come to the party, Mary won't go either. Am I correct?

Agent C
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