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blocks[s84,jmc]		The blocks world and axiomatization of common sense

	This is an outline of a talk given at SRI on 1984 June 8 at
the beginning of SRI's Common Sense Summer.

	This writeup is in lieu of a written version of the talk which
I hope one of the graduate students will be motivated to prepare with
my assistance.

	Common sense summer is concerned with writing axioms to describe
various aspects of the common sense world.  The "blocks world" is the
prototype domain for which axioms have been written to express common
sense knowledge about the effects of actions.  It has also been used
as a domain for natural language understanding (Winograd) and planning,
(see the AI Handbook, vol. 3 for references).

	In this lecture I want to advocate the situation calculus
formalism for writing axioms about the effects of actions.  If the
axioms are written with circumscription in mind, then the frame
problem is substantially solved.

	A situation, denoted by  s  perhaps with subscripts is taken
to be an instantaneous state of the world.  To fully describe a situation
would involve an infinite amount of knowledge, so we never do it.
Our statements only give facts about a situation or about the relations
between situations.  Formally this means that our axiom contains
no notation for fully describing situations.

	An example of asserting a fact about a situation is

(1)	on(Block1,Block2,S0)

which is taken to assert that  Block1  is on  Block2  in situation  S0.
We usually use  S0  to denote an initial situation before the events
whose effects we are interested in formalizing take place.

	There are various ways of writing these things with different
advantages.  One important set of axioms will express the above fact
as

(2)	location(Block1,S0) = top(Block2).

This extends the language by making locations as objects distinct from
blocks.  It therefore allows quantifying over locations.  (2) is a more
detailed description than (1) and it is possible to get still more
detailed ad infinitum.  There isn't a most detailed description
on which all others can be based.  Therefore, we should expect to
our common sense database to include formalisms at different levels
of detail and axioms giving the relations among them.

	Events occur in situations and produce new situations.  We
write

(3)	s' = result(e,s)

to assert that  s'  is the situation that results when event  e  occurs
in situation  s.

	A typical axiom might be approximately written

(4)	<precondition> ⊃ location(b1,result(move(b1,l),s) = l

asserting that if <precondition> is satisfied, then block  b1  is
in location  l  in the situation that results from moving it to  l.
We shall later say what these preconditions are.

	It being almost time for the lecture I will abandon this
level of detail and mention some topics that will be discussed
in the lecture.

	1. The situation calculus vs. other ways of writing action
axioms.

	2. The frame problem.

	3. The concept of the epistemological adequacy of a formalism.

	4. Using circumscription to write blocks world axioms.

	5. Extensions of the blocks world to include towers of blocks.
The relation between design and construction.

	6. Reification.

	7. The challenge problem of the dogs knocking over the trash cans.

	8. Axioms for heuristics.

	A main purpose of this lecture is to express the opinion
that it won't be feasible to just write down axioms giving the effects
of action unless one has a formalism in mind.  The situation calculus
provides a first approximation.