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McCarthy has continued his research on the theoretical foundations
of artificial intelligence, aimed at making computer programs
that can do common sense reasoning.  For this facts about the
common sense world, especially facts about the effects of actions
and facts about how knowledge is obtained, are repreented in
languages of mathematical logic.  A computer can then be programmed
to decide what to do by reasoning in logic to discover what course
of actions will best achieve the goals it has been given.  This
approach to artificial intelligence has proved very difficult, as
have all others, but important progress has been made recently
in the research supported by this grant.

Research on logical representation started in the 1950s, but in the
middle 1970s it became clear that an important extension of the
reasoning methods of mathematical logic would be required if
computer programs were to match human performance.  Mathematical
logical reasoning is {\it monotonic}.  This means that when
new premisses are added to a database, none of the previous
conclusions drawn from that database become invalid.  Common sense
reasoning is often non-monotonic and so is the reasoning computer
programs must draw from databases.  Before the 1970s when this
phenomenon was noticed, it was thought that such reasoning was
necessarily imprecise and therefore unsuited for computers.

Starting about 1977 various precise methods of non-monotonic
reasoning were proposed.  One of the main ones is {\it circumscription}
proposed by McCarthy, and during the period of this grant he
has developed it further and applied it to representing common
sense knowledge and common sense reasoning.  The results of this
work are summarized in the paper {\it Applications of circumscription
to formalizing common sense knowledge} that was presented at
the American Association for Artificial Intelligence workshop
on non-monotonic reasoning held in October 1984.