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Subject: Application of Predicate Logic to AI
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Here's an application of predicate logic to artificial intelligence (AI).

In the late 1950s, one of the founders of AI, John McCarthy, proposed a
computer program to be called "the advice taker", as part of a project
that he called "programs with common sense".  (This is a project that he
is still actively working on at the age of >= 80, by the way!)

(McCarthy is famous for at least the following things:  He came up with
the name "artificial intelligence", he invented the programming language
Lisp, and he invented time sharing.  For more information on him, link
to our "Logic" webpage at:

	http://www.cse.buffalo.edu/~rapaport/191/S09/logic.html

Then scroll down to:

	"John McCarthy's research on knowledge representation using FOL:"

and click on his name.)

The idea behind the advice taker was that problems to be solved would be
expressed in a predicate-logic language (only a little bit more
expressive than first-order predicate logic), then a set of premises or
assumptions describing required background information would be given,
and finally the problem would be solved by logically deducing it from
the assumptions.

He gave an example:  getting from his desk at home to the airport.  
It begins with premises like

	at(I,desk)

meaning "I am at my desk", and rules like 

	AxAyAz[(at(x,y) ^ at(y,z)) -> at(x,z)]

which expresses the transitivity of the "at" predicate, and slightly
more complicated rules (which go slightly beyond the expressive power
of FOL) like:

	AxAyAz[(walkable(x) ^ at(y,x) ^ at(z,x) ^ at(I,y))
					-> can(I, go(y,z,walking))]

i.e., if x is walkable, and y and z are at x, and I am at y,
      then I can go from y to z by walking.

The proposition to be proved from these (plus lots of others) is:

	want(at(I,airport))

To see it all worked out, take a look at his article:

McCarthy, John (1959), "Programs with Common Sense", in D.V. Blake &
A.M. Uttley (eds.), Proceedings of the ["Teddington"] Symposium on
Mechanisation of Thought Processes (London: HM Stationary Office).

There's a link to an online version at our Logic webpage:
http://www.cse.buffalo.edu/~rapaport/191/S09/logic.html