Discussion Groups / ESL Teaching / June 2006

You seek what is nonexistent.

You're going to have to decide, though, how much 'outside information'
to allow, since we don't utter sentences in complete isolation.  We
bring a huge amount of background knowledge to every interpretation of
every sentence.

Consider interpreting the sentence:
"Fred ate an ice-cream."

We already have the knowledge that "Fred" is probably a human
being.  Probably, but it's not certain.  If we met this sentence
out of nowhere, in perfect isolation, we would be best taking "Fred"
to be a human.  But if there were preceding context that identified
"Fred" as being a parrot, then that would have to be brought into the
interpretation and included in the 'equation' you're looking for.
It would alter the meaning and maybe even the truth or believability
of the sentence (thus affecting its usable information content).

Now, imagine if you met the following in the same perfectly
isolated context:
"Fred ate my homework."
We would need to know from 'outside information' that "Fred" is
now less likely to be a human.  There's nothing in the sentence
construction that changes this likelihood, so we *must* rely on
'outside information'.  In fact, very specific 'outside information'
(i.e., the cliché about my dog eating my homework) narrows the
interpretation even further.  The informational content of the
sentence now includes some implications that "Fred" is actually a
dog, not just that he ate my homework.  The information is there
to be extracted so isn't it a good idea to include it in any
equation suggested to derive the informational content?  To do so,
however, means working out some way of accommodating when and where
to use the 'outside information' we bring to the recovery of the
sentence's meaning.

Then, consider these sentences:
"The dog ate my letter."
"The fax machine ate my letter."
To work out what information these are giving us, we would need to
resort to things that are not explicitly stated in the sentences
themselves.

The short answer is that attempts to reduce natural language to neat
and tidy semantic formalisms are immensely difficult unless one is
willing to either:
1. Restrict the available definitions that your words can have
  (i.e., so every word can have one meaning and one meaning only)
  and/or restrict the type of sentences that you can process in
  this system (e.g., only process "X is Y" types).
Or:
2. Accept that there will be a whole heap of manual tweaking to
  make sure the intended interpretation is extracted (i.e., bring
  in all the unstated implications and presuppositions that we
  don't bother mentioning because the context and our own world-
  knowledge fill in the gaps).

However, you need that "outside information" in order to parse the
sentence.  Consider the canonical ambiguous sentence:

 Time flies like an arrow.

There are at least three ways of parsing that:

 Simile:
 
   time flies (verb) like (in a similar way) an arrow [flies]

 Eating habits:
 
   "time flies" (some sort of insect) like (verb) an arrow [to eat]
   (compare "fruit flies like a banana")

 Command:
 
   [You] time [those] flies like (in a similar way) an arrow [times
   flies]

Which is correct?  Only context can determine it, and not always then.

What you are asking for is a general algorithm for parsing natural
language.  It doesn't exist, if it did those who created it would be
making a lot of money.  But even humans can't unambiguously parse
natural language, as shown above, let alone put it into a
pseudo-mathematical language.  Even computer languages like Prolog still
have very rigid syntax compared to natural languages.

Note that the term 'equation' implies equality, as in your "raven =
black + bird", but that isn't the information actually conveyed by the
sentence "a raven is a black bird".  The actual information is more
complex, and is more accurately stated in English as "a raven is a type
of bird which is also black".  In a pseudo-mathematical form, where =>
is the relationship 'implies':

 raven => object(type=bird, colour=black)

A crow would also have the same description, as would a blackbird and
many others (assuming that the colour is the main colour, all of them
also have other colours as well, for instance yellow beaks).  It isn't
an equality, not all birds coloured black are ravens.

Chris C