Islands & Fuzzy Logic (was Re: Relative clauses and lambda calculus)

Trebor wrote:

<<
I recall you referring to "islands" before. What are they, exactly? And what
are some more English "island rules"?
>>
"Islands" are so-called because, figuratively, you can't walk off
an island.   Islands are certain types of phrases that arguments
can't be extracted from.   Note: This only applies to syntax that
holds that arguments *are* extracted.   For example:

Who did you see?

This sentence, in a syntax like Government and Binding or
Principles and Perameters (Minimalism too, I believe), is seen
as having a "deep" (or first) structure like this:

You did see who.

Through a variety of mechanisms (and they differ depending
on the syntax), "did" moves up in front of "you", and "who"
moves up in front of "did".

This works fine, unless the word "who" is in an "island".   In this
case, if you try to extract the word, the result is ungrammaticality.
So, for example:

*Who did you say your father trusted John and _ with the money?

The underscore is where the "who" came from.   It's in an island
(I believe an adjunct is the word I'm looking for), so if you try to
move the "who", a violation occurs.

There are five islands, if I remember right, and they're divided into
weak and strong island.   A weak island is an island where, if you
extract from it, the violation will be a little weaker.   Strong islands
result in strong violations.   [That is, based on speaker judgments.]
Each of the islands has names, and I found a website a long time
ago that explained them *beautifully*, but I can't find it!   I can't get
the right keywords.   Some examples on the net I've found:

(1) *Who did Mary wonder they will fire _?

(2) *Who did John meet the girl who will marry _?

These are examples of weak islands.   They're ungrammatical in
English, but it appears that they're grammatical in Greek:

http://216.239.57.104/search?q=cache:gVf1R-fgNDMJ:www.ling.ed.ac.uk/~theodora/
cls02.doc+strong+island+English+syntax&hl=en

I take that back.   I think (2) is a strong island.

Oh!   This seems like a good paper:

http://216.239.57.104/search?q=cache:QjsIHG_w2foJ:perso.wanadoo.fr/eric.mathie
u/Eric%2520Mathieu/vandeKootMathieu.pdf+weak+island+violation&hl=en

It has some good examples:

(3a) Reading this book to children is fun.
(3b) *Which book is reading _ to children fun?

(4a) John thanked the mechanic after he had repaired his car quickly.
(4b) *How did John thank the mechanic after he had repaired his car _?

Okay, my girlfriend just found my notes from that class, so now I
have some real information.   Here goes:

(1) Weak Islands:
(a) Rumor NP:
(i) I heard the rumor that Bob left.
(ii) */?Who did you hear the rumor that _ left?
[Note: The above sentence is grammatical for some.   Not me.]

(b) WH-Islands:
(i) I told him that she slept.
(ii) */?Who did I tell who slept?
[Note: Again, some people think this is okay.]

(2) Strong Islands:
(a) Sentential Subject:
(i) That she saw me amazes my mother.
(ii) *Who that _ saw me amazes my mother?
[Note: Even though this is a strong island, some find this okay.]

(b) Adjunct Islands:
(i) You said that Mary fixed the seat and Bob broke the car.
(ii) *What did you say that Mary fixed _ and Bob broke the car?
(iii) Mary fixed the car after Bob broke it.
(iv) *What did Mary fix _ after Bob broke _?
[Note: A resumptive pronoun might save (iv).]

(c) Relative Clause Islands:
(i) I told the man that you saw to leave my car alone.
(ii) *Who did I tell the man that _ saw to leave my car alone?
[Note: Violating this one is *really* bad.]

Those are the islands.   Violations differ depending on whether you
extract a subject or object.

Now, those are island constraints.   Languages differ on how bad
some are, or whether some are bad at all.   Most languages find all
strong island violations bad, but there are a couple that allow one or
two of them (I'm reminded of the term "super-raising").

Now, fuzzy logic.

According to formal semantics, all that matters is whether something
is true or false.   This seems find for sentences like "The boy sat down".
Either he did or he didn't.   But what about sentences like "The boy is
tall"?   To a baby, he is.   To a basketball player, he's short.   So what is
the truth value of the sentence "the boy is tall"?   Depends on who says
it.   Formal semantics are supposed to be context free, though, so you
shouldn't *have* to know who says something in order to figure out
its truth value.

Fuzzy logic was an attempt to incoporate gradations into context-free
semantics.   So, provided we're talking about a specific boy, then this
specific boy has a specific height.   Let's say he's four feet tall exactly
(I
don't know how tall this is in meters; sorry.   Like one meter and thirty
centimeters, or something).   Well, then, someone who's, let's say, three
feet tall and under will be likely to say that he's tall.   Anyone taller
than
that, though, will likely not say that he's tall.   (Note: It's not how many
people are taller than him.   I'm 5'8'', but I wouldn't call someone 5'9''
tall.)
In this way, you can get an approximation of the truth value.   So let's
say that someone who's four feet tall is "tall" to a degree of 0.1, or that
roughly 10% would agree that he was tall.   Now as you increase the height
of the person in question the percentage increases, and you have a
graph that is the truth value of tall.   Now you have a method for
calculating the truth value of "tall".

What this buys you is a method for interpreting things like:

A (5'5''): "Wow, that guy's tall!"
B (6'2''): "No he's not.   He's only an inch taller than me."

Both A's and B's utterances are true if you use themselves
as referents, but when applied to each other, their sentences
become false.

I used fuzzy logic in a paper I did last quarter on colloquial
"like".   Specifically, I analyzed a conversation I overheard:

A says about C's girlfriend: "She's, like, forty!"
B says: "No she's not.   She's, like, thirty."

What A meant, in effect, was that C's girlfriend is old.   B
responded by saying that she wasn't old.   The numbers
were what interested me, though.   Based on the group
this was said in, "forty" would be likely to be considered
"old" (I estimated that around 80% of people that were
that age would agree that forty was old), whereas "thirty"
would definitely not be.

[Actually, it was a bit more complicated than that.   I had
to come up with a graph of "old for C", the person in question,
which is the intersection of "old" and "appropriate age of a
girlfriend for C".   Or was that it...?   I forget now.]

Anyway, the point is that fuzzy logic allows one to calculate
previously incalculable truth values by adding the idea of varying
degrees of truth.

-David
*******************************************************************
"sunly eleSkarez ygralleryf ydZZixelje je ox2mejze."
"No eternal reward will forgive us now for wasting the dawn."

-Jim Morrison

http://dedalvs.free.fr/