I. Mixing knowledge representations
Large, robust AI systems typically don't rely on just
one approach to knowledge representation. We see this
in the example we began in the last lecture -- that of
trying to understand a simple story in English. This
problem can be decomposed into at least three distinct
problems (there are plenty more, but we'll leave it
at three for our purposes), each of which benefits from
a different knowledge representation approach.
Ultimately, the goal in language understanding is to
derive the meaning, both explicit and implicit, contained
in a given text. Often the first big step in such an
endeavour is to find the grammatical structure of the
individual sentences. Knowing the structure of the
sentence (and there may be many different structures
possible) helps constrain the search for meaning of
a that sentence. The process of decomposing a sentence
into its structural constituents is called parsing, and
a program that does so is a parser. In our example, we
represented simple knowledge about the structure of
sentences as a collection of rules written in CILOG.
Combined with CILOG's built-in reasoning system, we
have a simple example of a parser. This example
was adapted from Chapter 3.7 in your textbook. The
code is still a bit buggy; I haven't fixed it as I
said I should, but you can still get some sense of
how things work. It does run however, and you might
want to play with it a bit. This example also introduces
the use of function symbols which were explained in
Chapter 2.8, so you might want to read that soon.
Then we introduced the notion of the relational or
semantic network as a means of representing the
meanings of individual words.
II. Welcome to the relational network
We've been looking at tree-like data structures a lot
lately, and by now you're probably wondering what is the
big fascination with these things. The reason we get all
tingly about trees, or any sort of hierarchical data
structure, is that they're great ways to organize
knowledge. Traditional linear structures, like files with
lots of records, or even to some extent simple linear linked
lists like those we've been using in this class, make it
difficult to represent the wide variety of relationships
which exist between entities in the world. Trees get us a
step closer to representing the complexities of relationships
between things in the real world because they get us
closer to that notion of a relational network mentioned
above. Usually when we're building AI systems, we're really
trying to build models of some aspect of the real world, and
structures like trees help us make more useful models. Yet
trees are a bit constraining in the kinds of relationships
they permit between objects; a more general representation
is the network. A network is a labelled directed graph.
That is, it has nodes and arcs (or links), the links are
both directed and labelled, and there's no prohibition
against cycles. We can represent hierarchies in networks,
but more often we represent "tangled hierarchies".
III. Networks in the dictionary
We see hierarchical organizations in the real world all the
time. They may not be "pure" hierarchies, but they're
hierarchical in spirit at least. It might be easier to think
of these things as "networks" instead of hierarchies. Take
for example the common dictionary. At first glance, it looks
like a very linear organization of the words in our language.
But what a dictionary really specifies is a very complex
and somewhat hierarchical map of the relationships between
the words in our language. Here are some sample definitions:
dog: any of a large and varied group of domesticated animals
related to the fox, wolf, and jackal
chihuahua: any of an ancient Mexican breed of very small dog with
large, pointed ears
bird: any of a class of warm-blooded, two-legged, egg-laying
vertebrates with feathers and wings
penguin: any of an order of flight-less birds found in the Southern
Hemisphere, having webbed feet and paddle-like flippers for
swimming and diving
ostrich: a large, swift-running bird of Africa and the Near East; the
largest and most powerful of living birds; it has a long
neck, long legs, two toes on each foot, and small useless
wings
canary: a small yellow songbird of the finch family, native to the
Canary Islands
Notice that these definitions all relate the thing being
defined to some larger class of things, and then goes on to
try to distinguish that thing from other similar things. Note
also that as the things being described stray further and
further from what we might think of as being norms or
stereotypes, the definitions get longer and more detailed.
For example, compare the canary (a stereotypical bird) to an
ostrich (an extremely non-stereotypical bird).
When we take the time to look at the dictionary in this way,
we uncover what is essentially a bunch of pointers from one
word to others. Because I'm trying to prove a point here,
I've focused on the animal kingdom, knowing that zoologists
spend a lot of time building these "taxonomies", or
hierarchies of what is related to what. But it works for
things other than animals:
chair: a piece of furniture for one person to sit
on, having a back and, usually, four legs.
And so on. You can look up more if you like. Try "couch",
"sofa", "table", "ottoman", and whatever. No matter what noun
you look up, you'll find the same sort of pattern: relate
this word to a larger class of things, then describe some
features to distinguish this thing from similar sorts of
things.
The dictionary writers don't always help as much as we might like,
however:
rock: a large mass of stone
stone: the hard, solid, nonmetallic mineral matter that rock
is composed of
Except for the extra bit of information that stone is mineral
matter, all we know here is that rock is made of stone, and
stone is what makes up rock. Sigh.
In any case, we can use our high-level data abstraction, the
directed graph, to make these relationships a bit more
visual. For example, from the bird definitions, we can
construct the following abstraction:
vertebrate
^
| is-a
|
| has-part
| /------------- wings
| / reproduction
| /--------------- egg-laying
| / body-temp
| /----------------- warm-blooded
bird--<< no. of legs
^ ^ ^ \----------------- 2
/ | \ \ covering
is-a / | \ \--------------- feathers
/ | \ \ movement
color / | \ \------------- flight
yellow ------canary | \
size / | is-a \ is-a
small -----/ | \ movement
| ostrich---------- run
movement | \ size
swim ----------penguin \--------- big
OK, so I fudged this a little. I had to infer that the fact
that birds have wings means that they move around by flying;
the dictionary writers didn't tell us that. And I had to
infer that the fact that birds were egg-laying told us
something about their reproductive processes, and so on. But
you get the idea, no?
IV. Networks in your head
These sorts of knowledge hierarchies show up elsewhere.
Independent of this dictionary organization, psychologists in
the 1960s theorized that humans organize at least some of
what they know in a similar hierarchical fashion. For
example, they said, a person's knowledge of things in the
world might be organized along these lines:
all things
/ \
/ \
/ \
/ \
physical objects abstract objects
/ \ / \
/ \ / \
/ \ time thought
/ \
inanimate animate
objects objects
/ \ / \
/ \ / \
/ \ / \
inorganics plants mammals birds
/ \ / \ / \
/ \ / \ / \
rock car dog human canary ostrich
note: assume that all links point upward
This hierarchy is by no means complete, nor is it exactly
what the psychologists, Collins and Quillian, had proposed,
but it's sufficient for our purposes.
If we think of all the upward links as being relationships of
the form, "the thing below is a subtype of the thing above,"
then we have something called a "type hierarchy". And in
fact, we could put the label "subtype" or "subclass" on all
those upward links, to indicate that the thing below is a
"S"ubtype or "S"ubclass of the thing above. Folks in the AI
world don't use the "subclass" or "subtype" terminology very
much; instead, AI folks use the label "is-a" in hierarchies
like this, as in "a canary is-a bird". So these hierarchies
can also be called "is-a hierarchies". Note that we went
ahead and used that "is-a" label in the first diagram
above.
In any case, Collins and Quillian backed up their theory with
experiments based on this premise: If people really store
knowledge in hierarchical form, then if they're asked the
right questions, we should note significant differences in
the time it takes those people to respond correctly. For
example, the time to answer "yes" to "Is a canary a bird?"
should be less than the time to answer "yes" to "Is a canary
an animate object?"
The experiments did in fact generate the right numbers, and
for awhile everyone thought the question of how human memory
is organized had been answered. But other experimenters had
difficulty replicating these results, so there was some
controversy about just how Collins and Quillian obtained
their results. Nevertheless, hierarchical models of human
memory are still very popular, although they are somewhat
different in their organization than the one we've just
looked at.
V. Why do the arrows point up?
Well now, that's an interesting question, no? The reason, at
least from either a psychological or AI point of view, is
that humans typically are better at answering questions like
"Is a dog a mammal?" than questions like "Name all the
mammals you know." In other words, people are better at
recognition than recall or retrieval. The upward arrows in
our diagrams suggest that it would be easier to start at the
"dog" node and traverse the link up to the "mammal" node to
answer "Is a dog a mammal?", than it would be to start at the
"mammal" node and try to traverse all the downward links in
an effort to enumerate all the different types of mammals.
VI. Networks and relational databases
Everything we've shown you so far has been purely tree-like
in form, but as we've said, that's clearly not necessarily
going to be true. In fact, it's much more likely that the
organization in these structures will be much more
convoluted. Consider some of the relationships which may
exist in a small company that makes cough drops:
Smith options
Brothers ---------- pay plans
|\ / \
| \ / \
| \ salaried hourly
| \ / \ / \
dept.| ---- / $800/mo / $2.00/hr
| \ /
| pay / ---- /pay
| plan/ \ /plan
| / dept.\ /
| / \/
manufacturing shipping
/ \ / \
/ \ / \
/ \ / \
Arnie Brian Chuck David
Smith Smith Smith Smith
\
\ pay
\
$2.50/hr
In an ordinary database (often called a "flat-file" database)
where all the information about an employee is contained with
that employee's record, changing the pay rate for all the
salaried employees for example requires a change to every
salaried employee's record. In this database, changing every
salaried pay rate from $800 per month to $825 per month
requires only one change. Anyway, welcome to the exciting
world of relational databases. Relational database work is
something that evolved from artificial intelligence ideas
about how to organize knowledge (although you'll never get a
relational database person to admit this), which in turn
evolved from ideas in cognitive psychology.
VII. The whole world is one big graph
Geographically speaking, that's true. Take a look at
http://www.mapquest.com sometime and find a route between two
cities in the United States, say Atlanta and Los Angeles.
Now think about how Mapquest might find that route. Here's a
hint: look at a detailed highway map of the U.S....hmm, looks
like a network of cities and towns connected by roads, doesn't it?
And, you may have heard about the idea called "Six Degrees of
Separation"---that is, the idea that each of us is somehow
connected to everyone else on the planet by a distance of no
more than six personal or professional relationships. That
this notion might possibly be true suggests that, at least on
a relationship level, we can model the world's population as
a very very large directed graph, and that we could find a
specific connection between any two people by performing some
sort of search on that graph. That very principle is
embodied in the automated version of the once popular game
called "Six Degrees of Kevin Bacon" in which the premise is
that everyone in the film industry has no more than six
degrees of separation between them. You can try it out on
the World Wide Web at http://www.cs.virginia.edu/oracle
and while we're at it, the Web itself is just another
relational network structure...from a given Web site you can
link to a bunch of others, so you choose one, and from there
you can link to a bunch of others or go back, and so on. (If
you eliminate the commercial stuff, what's left on the Web
seems to be an interconnected network of narcissistic
memorials that people erect in honor of themselves...but I
digress.)
Last revised: December 7, 2004