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AIList Digest Volume 8 Issue 067
AIList Digest Friday, 26 Aug 1988 Volume 8 : Issue 67
Today's Topics:
English grammar: Open versus closed classes of words
Logic: Are all reasoning systems inconsistent?
Free Will: How to dispose of naive science types
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Date: Sat, 13 Aug 88 22:34:55 PDT
From: crocker@tis-w.arpa (Stephen D. Crocker)
Subject: open versus closed classes of words in English grammar
McGuire replied to Nagle's query about open versus closed classes of
words in English grammar, viz nouns, verbs, adjectives and adverbs are
open and conjunctions, articles, prepositions, etc. are closed. He then
comments:
> While I'm familiar with this distinction, and think that it may have
> been around in linguistics for quite some while (Bernard Bloch maybe?),
> I don't remember it being used much. The only references that spring to
> mind are some studies in speech production and slips of the tongue done
> in the 70s by Anne Cunningham (she's a Brit though I'm not sure of her
> last name) and maybe Victoria Fromkin claiming that less errors are
> associated with closed class words and that they play some privileged role
> in speech_production/syntax/lexical_access/the_archetecture_of_the_mind.
I recall in the mid or late 60's reading about a parser built in the UK that
relied heavily on the closed classes -- I think the term was "functions words".
I believe the parser determined which class the other words were in, noun,
verb, etc., solely by the slots created from the function words. To that
parser, McGuire's four example sentences would be equivalent to
"Foo frobbed fie"
"Foo has frobbed fie"
"Foo might frob fie"
"Foo fums to frob fie"
The parser was exceedingly fast, but I don't remember any follow up from
this work. If pressed, I can probably find a reference, but I suspect
many readers of this digest are more familiar with the work than I.
In the speech understanding work of the early 70's, I found it interesting
that the functions words played a lesser role than might have been expected
because they tended to be unstressed when spoken and hence reduced in duration
and clarity. I don't recall whether they played a major role in any of the
later systems. It's evident that humans depend on these words and learn
new open class words from context created by a combination of the closed
class words and known meanings for the open class words elsewhere in the
sentence. This suggests that one attribute to look for in truly mature
speech understanding systems is reliable "hearing" of function words. I'd
be interested if anyone knows the current status of speech understanding
in this area.
Along somewhat separate lines, Balzer at ISI built a rudimentary parser for
English in the early 70's. It was aimed at extracting formal program specs
from an English specification. His key example was based heavily on
interpeting the closed classes and treating the open classes as variables.
------------------------------
Date: Mon, 15 Aug 88 17:42
From: HILLS%reston.unisys.com@RELAY.CS.NET
Subject: Re: English Grammar
In AI List V8 #35 John Nagle described a grammar which divided words into
four catagories and requested a reference for the list of 'special' words.
This may be related to the work of Miller, Newman, and Friedman of Harvard.
In 1958 they proposed that words should be divided into two classes which they
defined as follows:
We will call these two classes the "function words" and the "content
words". Function words include those which are traditionally called
articles, prepositions, pronouns, conjunctions, and auxillary verbs,
plus certain irregular forms. The function words have rather specific
syntactic functions which must, by and large, be known individually
to the speaker of English. The content words include those which are
traditionally called nouns, verbs, and adjectives, plus most of the
adverbs. It is relatively easy to add new content words to a language,
but the set of function words is much more resistant to inovations.
The list of function words is included in the book: 'Elements of Software
Science' by Maurice H. Hallstead, Elsevier, 1977. This list contains about
330 words. I suspect that the list of 'special words' sought by Nagle is
contained within this list of function words.
-- Fred Hills
------------------------------
Date: 16 Aug 1988 08:06:55 EDT (Tue)
From: Ralph Hartley <hartley@nrl-aic.arpa>
Subject: Re: Are all reasoning systems inconsistent?
Your problem lies in T2
>T2. Aa[P(s("~P(*)",a)) -> ~P(a)] ; If I can prove that I can't prove X,
> then I can't prove X
This implies
Ea(~P(a))
i.e. that the system is consistent. Godel's 2nd (less well known) theorem
states that if it is possible to prove a system consistent within the system
then the system is NOT consistent. Therefore T2 cannot be a theorem in any
consistent system.
BTW - This is also a flaw in Hofstadter's reasoning about the prisoners dilema.
His argument goes as follows:
1. The other player uses the same reasoning as I do.
2. This reasoning produces a unique result (cooperate or defect but not both)
3. Therefor whatever I do he will do too.
4. So I should cooperate.
The problem, again, is that (1) and (2) imply that my logic is consistent -
therefore it is not.
Ralph Hartley
hartley@nrl-aic.ARPA
------------------------------
Date: 25 Aug 88 12:46:25 GMT
From: unido!sbsvax!yxoc@uunet.UU.NET (Ralf Treinen)
Subject: Re: Are all Reasoning Systems Inconsistent?
In a previous article, Jonathan Leivent writes:
> Here is a full version of the contradiction that I am claiming exists.
...
[ Q is the equality predicate, s is a substitution operation, "X" is the Godel ]
[ number of X ]
> P(a) : the predicate of provability within this reasoning system
...
> Theorems:
>
> T1. AaAb[Q(a,b)P(a) = P(b)] ; just says that P behaves normally
>
> T2. Aa[P(s("~P(*)",a)) -> ~P(a)] ; If I can prove that I can't prove X, then I
> can't prove X
>
> T3. If X can be proven within this reasoning system, then P("X") is true
[ "this reasoning system" is the original one together with (at least) T1,T2 ]
...
[ derives a contradiction by constructing a Godel number G, such that ~P(G) ]
[ can proven in the above system and then applying Theorem T3 ("step 5"). ]
...
> Perhaps the weak link in the contradiction is step 5, which is somewhat of a
> "meta" step. What bothers me most is that there seems to be no formal way of
> writing T3, even though it seems to be obviously true
...
Theorem T3 is not correct. Just take the empty reasoning system that doesn't
allow to derive any theorem at all. The provability predicate for this
reasoning system is the constant predicate *false*. The formula ~P(G)
constructed above is provable in the this system, but P("~P(G)") is false.
BTW: The empty reasoning system IS consistent.
--
------------------------------------------------------------------------------
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UUCP : ...!uunet!unido!sbsvax!treinen | Ralf Treinen
or treinen@sbsvax.UUCP | Universitaet des Saarlandes
CSNET: treinen%sbsvax.uucp@Germany.CSnet| FB 10 - Informatik (Dept. of CS)
ARPA : treinen%sbsvax.uucp@uunet.UU.NET | Bau 36, Im Stadtwald 15
Phone: +49 681 302 2065 | D-6600 Saarbruecken 11, West Germany
------------------------------
Date: 19 Aug 88 15:26:35 GMT
From: mcvax!ukc!cs.tcd.ie!tcdmath!dbell@uunet.uu.net (Derek Bell)
Subject: Re: How to dispose of naive science types (short)
In article <388@u1100s.UUCP> castle@u1100s.UUCP (Deborah Smit) writes:
>Another big mistake is when scientists present hypothetical OR theoretical
>work under the title "FACT". E.G. Evolution.
All theories can be regarded in that light, since it takes an
infinite amount of evvidence for one to be proved 100%. So, it all boils
down to: 1:What will someone accept as evidence?
2:How much/what kind will they take to be convinced,
if, at all?
>the title theory, since they are not demonstrable, and do not fit with
>the facts shown by the fossil record (no intermediate forms -- before
>you flame, examine current facts, fossils previously believed to be
>intermediate have been debunked). It certainly cannot be called FACT,
I was at a talk here where a paleontologist showed examples of
fossil trilobites of the various subspecies changed within a subspecies,
thus presenting evidence for 'microevolution', ie evolution within a species.
> When evolutionists cannot support their
>hypothesis by showing aggreement with known facts, they resort to
>emotional mind-bashing (only foolish, gullible people don't believe
>in evolution).
Whoa!!! Not all evolutionists, & not just evolutionists use
childish mind-bashing. Some creationsts do too.
> Just my two cents. I enjoy reasonable theories,
>they truly unify what we observe, but I don't appreciate emotional
>outbursts on the part of those who can't give up their inaccurate
>hypotheses to go on to something better.
> - Deborah Smit
This I agree with totally. Rational debate is far far better
than hysterical slanging matches.
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End of AIList Digest
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